(* Content-type: application/vnd.wolfram.mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 9.0' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       157,          7]
NotebookDataLength[     40296,       1118]
NotebookOptionsPosition[     39417,       1086]
NotebookOutlinePosition[     39762,       1101]
CellTagsIndexPosition[     39719,       1098]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{
Cell["\<\
Construct/Verify an example of a pair of anticommuting matrices each having a \
zero eigenvalue, and a shared eigenvector.\
\>", "Text",
 CellChangeTimes->{{3.6524826765223866`*^9, 3.6524827249175396`*^9}, {
  3.6524828509526625`*^9, 3.6524828519070644`*^9}}],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"ClearAll", "[", 
   RowBox[{"a", ",", " ", "b", ",", " ", "e", ",", " ", "d", ",", " ", "h"}], 
   "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"d", " ", "=", " ", "1"}], " ", ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"a", " ", "=", " ", 
   RowBox[{"DiagonalMatrix", "[", 
    RowBox[{"{", 
     RowBox[{"1", ",", 
      RowBox[{"-", "1"}], ",", "d"}], "}"}], "]"}]}], " ", 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"b", " ", "=", " ", 
   RowBox[{"DiagonalMatrix", "[", 
    RowBox[{"{", 
     RowBox[{"0", ",", "0", ",", "d"}], "}"}], "]"}]}], " ", 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"h", " ", "=", " ", 
   RowBox[{"DiagonalMatrix", "[", 
    RowBox[{"{", 
     RowBox[{"0", ",", "0", ",", "1"}], "}"}], "]"}]}], " ", 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"b", "[", 
    RowBox[{"[", 
     RowBox[{"1", ",", "2"}], "]"}], "]"}], " ", "=", " ", "1"}], " ", 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"b", "[", 
    RowBox[{"[", 
     RowBox[{"2", ",", "1"}], "]"}], "]"}], " ", "=", " ", "1"}], " ", 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Grid", "[", 
   RowBox[{"{", "\[IndentingNewLine]", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"\"\<A = \>\"", ",", "\[IndentingNewLine]", 
       RowBox[{"a", " ", "//", " ", "MatrixForm"}]}], "}"}], ",", 
     "\[IndentingNewLine]", 
     RowBox[{"{", 
      RowBox[{"\"\<B = \>\"", ",", "\[IndentingNewLine]", 
       RowBox[{"b", " ", "//", " ", "MatrixForm"}]}], "}"}], ",", 
     "\[IndentingNewLine]", 
     RowBox[{"{", 
      RowBox[{"\"\<{A,B} = \>\"", ",", "\[IndentingNewLine]", 
       RowBox[{
        RowBox[{
         RowBox[{"a", " ", ".", "b"}], " ", "+", " ", 
         RowBox[{"b", " ", ".", "a"}]}], " ", "//", " ", "MatrixForm"}]}], 
      "}"}], ",", "\[IndentingNewLine]", 
     RowBox[{"{", 
      RowBox[{"\"\<[A,B] = \>\"", ",", "\[IndentingNewLine]", 
       RowBox[{
        RowBox[{
         RowBox[{"a", " ", ".", "b"}], " ", "-", " ", 
         RowBox[{"b", " ", ".", "a"}]}], " ", "//", " ", "MatrixForm"}]}], 
      "}"}], ",", "\[IndentingNewLine]", 
     RowBox[{"{", 
      RowBox[{"\"\<{A,H} = \>\"", ",", "\[IndentingNewLine]", 
       RowBox[{
        RowBox[{
         RowBox[{"a", " ", ".", "h"}], " ", "+", " ", 
         RowBox[{"h", " ", ".", "a"}]}], " ", "//", " ", "MatrixForm"}]}], 
      "}"}], ",", "\[IndentingNewLine]", 
     RowBox[{"{", 
      RowBox[{"\"\<[A,H] = \>\"", ",", "\[IndentingNewLine]", 
       RowBox[{
        RowBox[{
         RowBox[{"a", " ", ".", "h"}], " ", "-", " ", 
         RowBox[{"h", " ", ".", "a"}]}], " ", "//", " ", "MatrixForm"}]}], 
      "}"}], ",", "\[IndentingNewLine]", 
     RowBox[{"{", 
      RowBox[{"\"\<{B,H} = \>\"", ",", "\[IndentingNewLine]", 
       RowBox[{
        RowBox[{
         RowBox[{"b", " ", ".", "h"}], " ", "+", " ", 
         RowBox[{"h", " ", ".", "b"}]}], " ", "//", " ", "MatrixForm"}]}], 
      "}"}], ",", "\[IndentingNewLine]", 
     RowBox[{"{", 
      RowBox[{"\"\<[B,H] = \>\"", ",", "\[IndentingNewLine]", 
       RowBox[{
        RowBox[{
         RowBox[{"b", " ", ".", "h"}], " ", "-", " ", 
         RowBox[{"h", " ", ".", "b"}]}], " ", "//", " ", "MatrixForm"}]}], 
      "}"}]}], "}"}], " ", "]"}], " ", 
  "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{"Eigensystem", "[", "a", "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Eigensystem", "[", "b", "]"}], 
  "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"e", "  ", "=", " ", 
   RowBox[{"{", 
    RowBox[{"0", ",", "0", ",", "1"}], "}"}]}], " ", 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"a", " ", "e"}], " ", "//", " ", 
  "MatrixForm"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"b", " ", "e"}], " ", "//", " ", 
  "MatrixForm"}], "\[IndentingNewLine]"}], "Input",
 CellChangeTimes->{{3.65248253506796*^9, 3.6524826193722305`*^9}, {
  3.654512858304221*^9, 3.654512944308672*^9}, {3.65451297911874*^9, 
  3.6545129791437597`*^9}, {3.6545130112381215`*^9, 3.654513011295169*^9}, {
  3.6545130460482845`*^9, 3.6545130508005733`*^9}, {3.6545134854465466`*^9, 
  3.654513489096841*^9}, {3.6545135192629027`*^9, 3.654513618735325*^9}, {
  3.654513849457674*^9, 3.654513907854181*^9}}],

Cell[BoxData[
 TagBox[GridBox[{
    {"\<\"A = \"\>", 
     TagBox[
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"1", "0", "0"},
         {"0", 
          RowBox[{"-", "1"}], "0"},
         {"0", "0", "1"}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
      Function[BoxForm`e$, 
       MatrixForm[BoxForm`e$]]]},
    {"\<\"B = \"\>", 
     TagBox[
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"0", "1", "0"},
         {"1", "0", "0"},
         {"0", "0", "1"}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
      Function[BoxForm`e$, 
       MatrixForm[BoxForm`e$]]]},
    {"\<\"{A,B} = \"\>", 
     TagBox[
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"0", "0", "0"},
         {"0", "0", "0"},
         {"0", "0", "2"}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
      Function[BoxForm`e$, 
       MatrixForm[BoxForm`e$]]]},
    {"\<\"[A,B] = \"\>", 
     TagBox[
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"0", "2", "0"},
         {
          RowBox[{"-", "2"}], "0", "0"},
         {"0", "0", "0"}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
      Function[BoxForm`e$, 
       MatrixForm[BoxForm`e$]]]},
    {"\<\"{A,H} = \"\>", 
     TagBox[
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"0", "0", "0"},
         {"0", "0", "0"},
         {"0", "0", "2"}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
      Function[BoxForm`e$, 
       MatrixForm[BoxForm`e$]]]},
    {"\<\"[A,H] = \"\>", 
     TagBox[
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"0", "0", "0"},
         {"0", "0", "0"},
         {"0", "0", "0"}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
      Function[BoxForm`e$, 
       MatrixForm[BoxForm`e$]]]},
    {"\<\"{B,H} = \"\>", 
     TagBox[
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"0", "0", "0"},
         {"0", "0", "0"},
         {"0", "0", "2"}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
      Function[BoxForm`e$, 
       MatrixForm[BoxForm`e$]]]},
    {"\<\"[B,H] = \"\>", 
     TagBox[
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"0", "0", "0"},
         {"0", "0", "0"},
         {"0", "0", "0"}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
      Function[BoxForm`e$, 
       MatrixForm[BoxForm`e$]]]}
   },
   AutoDelete->False,
   GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}],
  "Grid"]], "Output",
 CellChangeTimes->{{3.6524825689695253`*^9, 3.652482589811301*^9}, 
   3.6524826209054995`*^9, 3.654512947242321*^9, {3.654512981767354*^9, 
   3.6545130122079935`*^9}, 3.6545132754011345`*^9, 3.6545134898835526`*^9, 
   3.6545135352595253`*^9, {3.654513604197204*^9, 3.6545136202396965`*^9}, 
   3.654513704723833*^9, 3.654513852523385*^9, 3.654513916492979*^9}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     RowBox[{"-", "1"}], ",", "1", ",", "1"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"0", ",", "1", ",", "0"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"0", ",", "0", ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"1", ",", "0", ",", "0"}], "}"}]}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{{3.6524825689695253`*^9, 3.652482589811301*^9}, 
   3.6524826209054995`*^9, 3.654512947242321*^9, {3.654512981767354*^9, 
   3.6545130122079935`*^9}, 3.6545132754011345`*^9, 3.6545134898835526`*^9, 
   3.6545135352595253`*^9, {3.654513604197204*^9, 3.6545136202396965`*^9}, 
   3.654513704723833*^9, 3.654513852523385*^9, 3.6545139165210047`*^9}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     RowBox[{"-", "1"}], ",", "1", ",", "1"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{
       RowBox[{"-", "1"}], ",", "1", ",", "0"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"0", ",", "0", ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"1", ",", "1", ",", "0"}], "}"}]}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{{3.6524825689695253`*^9, 3.652482589811301*^9}, 
   3.6524826209054995`*^9, 3.654512947242321*^9, {3.654512981767354*^9, 
   3.6545130122079935`*^9}, 3.6545132754011345`*^9, 3.6545134898835526`*^9, 
   3.6545135352595253`*^9, {3.654513604197204*^9, 3.6545136202396965`*^9}, 
   3.654513704723833*^9, 3.654513852523385*^9, 3.6545139165400677`*^9}],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {"0", "0", "0"},
     {"0", "0", "0"},
     {"0", "0", "1"}
    },
    GridBoxAlignment->{
     "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
      "RowsIndexed" -> {}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{{3.6524825689695253`*^9, 3.652482589811301*^9}, 
   3.6524826209054995`*^9, 3.654512947242321*^9, {3.654512981767354*^9, 
   3.6545130122079935`*^9}, 3.6545132754011345`*^9, 3.6545134898835526`*^9, 
   3.6545135352595253`*^9, {3.654513604197204*^9, 3.6545136202396965`*^9}, 
   3.654513704723833*^9, 3.654513852523385*^9, 3.654513916561041*^9}],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {"0", "0", "0"},
     {"0", "0", "0"},
     {"0", "0", "1"}
    },
    GridBoxAlignment->{
     "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
      "RowsIndexed" -> {}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{{3.6524825689695253`*^9, 3.652482589811301*^9}, 
   3.6524826209054995`*^9, 3.654512947242321*^9, {3.654512981767354*^9, 
   3.6545130122079935`*^9}, 3.6545132754011345`*^9, 3.6545134898835526`*^9, 
   3.6545135352595253`*^9, {3.654513604197204*^9, 3.6545136202396965`*^9}, 
   3.654513704723833*^9, 3.654513852523385*^9, 3.654513916583057*^9}]
}, Open  ]],

Cell["\<\
Check syntax.  These should not commute:\
\>", "Text",
 CellChangeTimes->{{3.6545130770462713`*^9, 3.654513121513435*^9}, {
  3.654513643578193*^9, 3.654513666346094*^9}}],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"ClearAll", "[", 
  RowBox[{"x", ",", " ", "z"}], "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"z", " ", "=", " ", 
   RowBox[{"DiagonalMatrix", "[", 
    RowBox[{"{", 
     RowBox[{"1", ",", 
      RowBox[{"-", "1"}]}], "}"}], "]"}]}], " ", ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"x", " ", "=", " ", 
   RowBox[{"DiagonalMatrix", "[", 
    RowBox[{"{", 
     RowBox[{"0", ",", "0"}], "}"}], "]"}]}], " ", 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"x", "[", 
    RowBox[{"[", 
     RowBox[{"1", ",", "2"}], "]"}], "]"}], " ", "=", " ", "1"}], " ", 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"x", "[", 
    RowBox[{"[", 
     RowBox[{"2", ",", "1"}], "]"}], "]"}], " ", "=", " ", "1"}], " ", 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Grid", "[", 
   RowBox[{"{", "\[IndentingNewLine]", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"\"\<x = \>\"", ",", "\[IndentingNewLine]", 
       RowBox[{"x", " ", "//", " ", "MatrixForm"}]}], "}"}], ",", 
     "\[IndentingNewLine]", 
     RowBox[{"{", 
      RowBox[{"\"\<z = \>\"", ",", "\[IndentingNewLine]", 
       RowBox[{"z", " ", "//", " ", "MatrixForm"}]}], "}"}], ",", 
     "\[IndentingNewLine]", 
     RowBox[{"{", 
      RowBox[{"\"\<{x,z} = \>\"", ",", "\[IndentingNewLine]", 
       RowBox[{
        RowBox[{
         RowBox[{"x", ".", " ", "z"}], " ", "+", " ", 
         RowBox[{"z", " ", ".", "x"}]}], " ", "//", " ", "MatrixForm"}]}], 
      "}"}], ",", " ", 
     RowBox[{"(*", 
      RowBox[{"needed", " ", "dots", " ", "between", " ", 
       RowBox[{"products", "!"}]}], "*)"}], "\[IndentingNewLine]", 
     RowBox[{"{", 
      RowBox[{"\"\<[x,z] = \>\"", ",", "\[IndentingNewLine]", 
       RowBox[{
        RowBox[{
         RowBox[{"x", " ", ".", "z"}], " ", "-", " ", 
         RowBox[{"z", " ", ".", "x"}]}], " ", "//", " ", "MatrixForm"}]}], 
      "}"}]}], "}"}], " ", "]"}], " "}]}], "Input",
 CellChangeTimes->{{3.654513127975268*^9, 3.6545131535560937`*^9}, {
  3.654513383467331*^9, 3.65451347072024*^9}, {3.654513670160516*^9, 
  3.65451368245547*^9}}],

Cell[BoxData[
 TagBox[GridBox[{
    {"\<\"x = \"\>", 
     TagBox[
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"0", "1"},
         {"1", "0"}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
      Function[BoxForm`e$, 
       MatrixForm[BoxForm`e$]]]},
    {"\<\"z = \"\>", 
     TagBox[
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"1", "0"},
         {"0", 
          RowBox[{"-", "1"}]}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
      Function[BoxForm`e$, 
       MatrixForm[BoxForm`e$]]]},
    {"\<\"{x,z} = \"\>", 
     TagBox[
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"0", "0"},
         {"0", "0"}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
      Function[BoxForm`e$, 
       MatrixForm[BoxForm`e$]]]},
    {"\<\"[x,z] = \"\>", 
     TagBox[
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"0", 
          RowBox[{"-", "2"}]},
         {"2", "0"}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
      Function[BoxForm`e$, 
       MatrixForm[BoxForm`e$]]]}
   },
   AutoDelete->False,
   GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}],
  "Grid"]], "Output",
 CellChangeTimes->{{3.654513446466718*^9, 3.654513471442894*^9}}]
}, Open  ]],

Cell["\<\
Counter example for Shankar 1.17 ?\
\>", "Text",
 CellChangeTimes->{{3.654514457551799*^9, 3.6545144759098697`*^9}, {
  3.654514652674958*^9, 3.6545146529281893`*^9}}],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"ClearAll", "[", 
   RowBox[{"a", ",", " ", "b", ",", " ", "h"}], "]"}], 
  "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"a", " ", "=", " ", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"0", ",", "1"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"0", ",", "0"}], "}"}]}], "}"}]}], " ", 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"b", " ", "=", " ", 
   RowBox[{"DiagonalMatrix", "[", 
    RowBox[{"{", 
     RowBox[{"1", ",", "0"}], "}"}], "]"}]}], " ", 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"h", " ", "=", " ", 
    RowBox[{"DiagonalMatrix", "[", 
     RowBox[{"{", 
      RowBox[{"0", ",", "0"}], "}"}], "]"}]}], " ", ";"}], 
  "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Grid", "[", 
   RowBox[{"{", "\[IndentingNewLine]", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"\"\<A = \>\"", ",", "\[IndentingNewLine]", 
       RowBox[{"a", " ", "//", " ", "MatrixForm"}]}], "}"}], ",", 
     "\[IndentingNewLine]", 
     RowBox[{"{", 
      RowBox[{"\"\<B = \>\"", ",", "\[IndentingNewLine]", 
       RowBox[{"b", " ", "//", " ", "MatrixForm"}]}], "}"}], ",", 
     "\[IndentingNewLine]", 
     RowBox[{"{", 
      RowBox[{"\"\<H = \>\"", ",", "\[IndentingNewLine]", 
       RowBox[{"h", " ", "//", " ", "MatrixForm"}]}], "}"}], ",", 
     "\[IndentingNewLine]", 
     RowBox[{"{", 
      RowBox[{"\"\<{A,B} = \>\"", ",", "\[IndentingNewLine]", 
       RowBox[{
        RowBox[{
         RowBox[{"a", " ", ".", "b"}], " ", "+", " ", 
         RowBox[{"b", " ", ".", "a"}]}], " ", "//", " ", "MatrixForm"}]}], 
      "}"}], ",", "\[IndentingNewLine]", 
     RowBox[{"{", 
      RowBox[{"\"\<[A,B] = \>\"", ",", "\[IndentingNewLine]", 
       RowBox[{
        RowBox[{
         RowBox[{"a", " ", ".", "b"}], " ", "-", " ", 
         RowBox[{"b", " ", ".", "a"}]}], " ", "//", " ", "MatrixForm"}]}], 
      "}"}], ",", "\[IndentingNewLine]", 
     RowBox[{"{", 
      RowBox[{"\"\<{A,H} = \>\"", ",", "\[IndentingNewLine]", 
       RowBox[{
        RowBox[{
         RowBox[{"a", " ", ".", "h"}], " ", "+", " ", 
         RowBox[{"h", " ", ".", "a"}]}], " ", "//", " ", "MatrixForm"}]}], 
      "}"}], ",", "\[IndentingNewLine]", 
     RowBox[{"{", 
      RowBox[{"\"\<[A,H] = \>\"", ",", "\[IndentingNewLine]", 
       RowBox[{
        RowBox[{
         RowBox[{"a", " ", ".", "h"}], " ", "-", " ", 
         RowBox[{"h", " ", ".", "a"}]}], " ", "//", " ", "MatrixForm"}]}], 
      "}"}], ",", "\[IndentingNewLine]", 
     RowBox[{"{", 
      RowBox[{"\"\<{B,H} = \>\"", ",", "\[IndentingNewLine]", 
       RowBox[{
        RowBox[{
         RowBox[{"b", " ", ".", "h"}], " ", "+", " ", 
         RowBox[{"h", " ", ".", "b"}]}], " ", "//", " ", "MatrixForm"}]}], 
      "}"}], ",", "\[IndentingNewLine]", 
     RowBox[{"{", 
      RowBox[{"\"\<[B,H] = \>\"", ",", "\[IndentingNewLine]", 
       RowBox[{
        RowBox[{
         RowBox[{"b", " ", ".", "h"}], " ", "-", " ", 
         RowBox[{"h", " ", ".", "b"}]}], " ", "//", " ", "MatrixForm"}]}], 
      "}"}]}], "}"}], " ", "]"}], " ", 
  "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"a", " ", "=", " ", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"0", ",", "1", ",", " ", "0"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"0", ",", "0", ",", " ", "0"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"0", ",", "0", ",", " ", "1"}], "}"}]}], "}"}]}], " ", 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"b", " ", "=", " ", 
   RowBox[{"DiagonalMatrix", "[", 
    RowBox[{"{", 
     RowBox[{"1", ",", "0", ",", " ", "1"}], "}"}], "]"}]}], " ", 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"h", " ", "=", " ", 
    RowBox[{"DiagonalMatrix", "[", 
     RowBox[{"{", 
      RowBox[{"0", ",", "0", ",", " ", "1"}], "}"}], "]"}]}], " ", ";"}], 
  "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Grid", "[", 
   RowBox[{"{", "\[IndentingNewLine]", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"\"\<A = \>\"", ",", "\[IndentingNewLine]", 
       RowBox[{"a", " ", "//", " ", "MatrixForm"}]}], "}"}], ",", 
     "\[IndentingNewLine]", 
     RowBox[{"{", 
      RowBox[{"\"\<B = \>\"", ",", "\[IndentingNewLine]", 
       RowBox[{"b", " ", "//", " ", "MatrixForm"}]}], "}"}], ",", 
     "\[IndentingNewLine]", 
     RowBox[{"{", 
      RowBox[{"\"\<H = \>\"", ",", "\[IndentingNewLine]", 
       RowBox[{"h", " ", "//", " ", "MatrixForm"}]}], "}"}], ",", 
     "\[IndentingNewLine]", 
     RowBox[{"{", 
      RowBox[{"\"\<{A,B} = \>\"", ",", "\[IndentingNewLine]", 
       RowBox[{
        RowBox[{
         RowBox[{"a", " ", ".", "b"}], " ", "+", " ", 
         RowBox[{"b", " ", ".", "a"}]}], " ", "//", " ", "MatrixForm"}]}], 
      "}"}], ",", "\[IndentingNewLine]", 
     RowBox[{"{", 
      RowBox[{"\"\<[A,B] = \>\"", ",", "\[IndentingNewLine]", 
       RowBox[{
        RowBox[{
         RowBox[{"a", " ", ".", "b"}], " ", "-", " ", 
         RowBox[{"b", " ", ".", "a"}]}], " ", "//", " ", "MatrixForm"}]}], 
      "}"}], ",", "\[IndentingNewLine]", 
     RowBox[{"{", 
      RowBox[{"\"\<{A,H} = \>\"", ",", "\[IndentingNewLine]", 
       RowBox[{
        RowBox[{
         RowBox[{"a", " ", ".", "h"}], " ", "+", " ", 
         RowBox[{"h", " ", ".", "a"}]}], " ", "//", " ", "MatrixForm"}]}], 
      "}"}], ",", "\[IndentingNewLine]", 
     RowBox[{"{", 
      RowBox[{"\"\<[A,H] = \>\"", ",", "\[IndentingNewLine]", 
       RowBox[{
        RowBox[{
         RowBox[{"a", " ", ".", "h"}], " ", "-", " ", 
         RowBox[{"h", " ", ".", "a"}]}], " ", "//", " ", "MatrixForm"}]}], 
      "}"}], ",", "\[IndentingNewLine]", 
     RowBox[{"{", 
      RowBox[{"\"\<{B,H} = \>\"", ",", "\[IndentingNewLine]", 
       RowBox[{
        RowBox[{
         RowBox[{"b", " ", ".", "h"}], " ", "+", " ", 
         RowBox[{"h", " ", ".", "b"}]}], " ", "//", " ", "MatrixForm"}]}], 
      "}"}], ",", "\[IndentingNewLine]", 
     RowBox[{"{", 
      RowBox[{"\"\<[B,H] = \>\"", ",", "\[IndentingNewLine]", 
       RowBox[{
        RowBox[{
         RowBox[{"b", " ", ".", "h"}], " ", "-", " ", 
         RowBox[{"h", " ", ".", "b"}]}], " ", "//", " ", "MatrixForm"}]}], 
      "}"}]}], "}"}], " ", "]"}], " "}]}], "Input",
 CellChangeTimes->{{3.6545144881508694`*^9, 3.6545145662562475`*^9}, 
   3.6545145969068885`*^9, {3.6545146624638023`*^9, 3.654514687535575*^9}}],

Cell[BoxData[
 TagBox[GridBox[{
    {"\<\"A = \"\>", 
     TagBox[
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"0", "1"},
         {"0", "0"}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
      Function[BoxForm`e$, 
       MatrixForm[BoxForm`e$]]]},
    {"\<\"B = \"\>", 
     TagBox[
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"1", "0"},
         {"0", "0"}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
      Function[BoxForm`e$, 
       MatrixForm[BoxForm`e$]]]},
    {"\<\"H = \"\>", 
     TagBox[
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"0", "0"},
         {"0", "0"}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
      Function[BoxForm`e$, 
       MatrixForm[BoxForm`e$]]]},
    {"\<\"{A,B} = \"\>", 
     TagBox[
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"0", "1"},
         {"0", "0"}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
      Function[BoxForm`e$, 
       MatrixForm[BoxForm`e$]]]},
    {"\<\"[A,B] = \"\>", 
     TagBox[
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"0", 
          RowBox[{"-", "1"}]},
         {"0", "0"}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
      Function[BoxForm`e$, 
       MatrixForm[BoxForm`e$]]]},
    {"\<\"{A,H} = \"\>", 
     TagBox[
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"0", "0"},
         {"0", "0"}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
      Function[BoxForm`e$, 
       MatrixForm[BoxForm`e$]]]},
    {"\<\"[A,H] = \"\>", 
     TagBox[
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"0", "0"},
         {"0", "0"}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
      Function[BoxForm`e$, 
       MatrixForm[BoxForm`e$]]]},
    {"\<\"{B,H} = \"\>", 
     TagBox[
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"0", "0"},
         {"0", "0"}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
      Function[BoxForm`e$, 
       MatrixForm[BoxForm`e$]]]},
    {"\<\"[B,H] = \"\>", 
     TagBox[
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"0", "0"},
         {"0", "0"}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
      Function[BoxForm`e$, 
       MatrixForm[BoxForm`e$]]]}
   },
   AutoDelete->False,
   GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}],
  "Grid"]], "Output",
 CellChangeTimes->{{3.654514571740159*^9, 3.654514599110875*^9}, 
   3.6545146885265045`*^9}],

Cell[BoxData[
 TagBox[GridBox[{
    {"\<\"A = \"\>", 
     TagBox[
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"0", "1", "0"},
         {"0", "0", "0"},
         {"0", "0", "1"}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
      Function[BoxForm`e$, 
       MatrixForm[BoxForm`e$]]]},
    {"\<\"B = \"\>", 
     TagBox[
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"1", "0", "0"},
         {"0", "0", "0"},
         {"0", "0", "1"}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
      Function[BoxForm`e$, 
       MatrixForm[BoxForm`e$]]]},
    {"\<\"H = \"\>", 
     TagBox[
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"0", "0", "0"},
         {"0", "0", "0"},
         {"0", "0", "1"}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
      Function[BoxForm`e$, 
       MatrixForm[BoxForm`e$]]]},
    {"\<\"{A,B} = \"\>", 
     TagBox[
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"0", "1", "0"},
         {"0", "0", "0"},
         {"0", "0", "2"}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
      Function[BoxForm`e$, 
       MatrixForm[BoxForm`e$]]]},
    {"\<\"[A,B] = \"\>", 
     TagBox[
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"0", 
          RowBox[{"-", "1"}], "0"},
         {"0", "0", "0"},
         {"0", "0", "0"}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
      Function[BoxForm`e$, 
       MatrixForm[BoxForm`e$]]]},
    {"\<\"{A,H} = \"\>", 
     TagBox[
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"0", "0", "0"},
         {"0", "0", "0"},
         {"0", "0", "2"}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
      Function[BoxForm`e$, 
       MatrixForm[BoxForm`e$]]]},
    {"\<\"[A,H] = \"\>", 
     TagBox[
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"0", "0", "0"},
         {"0", "0", "0"},
         {"0", "0", "0"}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
      Function[BoxForm`e$, 
       MatrixForm[BoxForm`e$]]]},
    {"\<\"{B,H} = \"\>", 
     TagBox[
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"0", "0", "0"},
         {"0", "0", "0"},
         {"0", "0", "2"}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
      Function[BoxForm`e$, 
       MatrixForm[BoxForm`e$]]]},
    {"\<\"[B,H] = \"\>", 
     TagBox[
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"0", "0", "0"},
         {"0", "0", "0"},
         {"0", "0", "0"}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
      Function[BoxForm`e$, 
       MatrixForm[BoxForm`e$]]]}
   },
   AutoDelete->False,
   GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}],
  "Grid"]], "Output",
 CellChangeTimes->{{3.654514571740159*^9, 3.654514599110875*^9}, 
   3.6545146886205626`*^9}]
}, Open  ]]
},
WindowSize->{707, 636},
WindowMargins->{{Automatic, 174}, {46, Automatic}},
FrontEndVersion->"9.0 for Microsoft Windows (64-bit) (January 25, 2013)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[557, 20, 269, 5, 66, "Text"],
Cell[CellGroupData[{
Cell[851, 29, 4338, 113, 841, "Input"],
Cell[5192, 144, 6100, 164, 527, "Output"],
Cell[11295, 310, 767, 18, 40, "Output"],
Cell[12065, 330, 790, 19, 40, "Output"],
Cell[12858, 351, 981, 23, 96, "Output"],
Cell[13842, 376, 981, 23, 96, "Output"]
}, Open  ]],
Cell[14838, 402, 181, 4, 40, "Text"],
Cell[CellGroupData[{
Cell[15044, 410, 2127, 58, 391, "Input"],
Cell[17174, 470, 2890, 80, 183, "Output"]
}, Open  ]],
Cell[20079, 553, 177, 4, 40, "Text"],
Cell[CellGroupData[{
Cell[20281, 561, 6454, 169, 1241, "Input"],
Cell[26738, 732, 6168, 170, 393, "Output"],
Cell[32909, 904, 6492, 179, 591, "Output"]
}, Open  ]]
}
]
*)

(* End of internal cache information *)