14
$\begingroup$

Given a matrix, A:

A = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}};

How can I do the matrix multiplication A times A step by step?

$\endgroup$
1
34
$\begingroup$

If you have Mathematica 10 you can use the new Inactive functionality

step1 = MatrixForm[Inner[Inactive[Times], A, A, Inactive[Plus]], TableSpacing -> {3, 3}]

enter image description here

step2 = Activate[step1, Times]

enter image description here

Activate[step2]

enter image description here

$\endgroup$
1
  • 2
    $\begingroup$ Dang, I was trying to figure out how to use Inactivate on Plus and Times to get this to work with Inner, but it wasn't working because I was placing Inactive at the wrong locations of my expression. +1 for getting it to work! $\endgroup$ – DumpsterDoofus Oct 5 '14 at 16:19
15
$\begingroup$

You can use HoldForm or Defer with Composition if you are still using Pre V10 versions:

MatrixForm[Inner[Composition[Defer, Times], A, A, 
                              Composition[Defer, Plus]], TableSpacing -> {3, 3}]

Mathematica graphics

MatrixForm[Inner[Times, A, A, Composition[HoldForm, Plus]], TableSpacing -> {3, 3}]

Mathematica graphics

MatrixForm[Inner[Times, A, A, Plus], TableSpacing -> {3, 3}]

Mathematica graphics

Of course, there's the V10 syntax for Composition i.e. @* that can make the above code shorter:

MatrixForm[Inner[Defer@*Times, A, A, Defer@*Plus], TableSpacing -> {3, 3}]
MatrixForm[Inner[Times, A, A, Defer@*Plus], TableSpacing -> {3, 3}]
MatrixForm[Inner[Times, A, A, Plus], TableSpacing -> {3, 3}]
$\endgroup$
2
$\begingroup$
Clear[A, n, k, nn, aa]
A = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}};
Print["A"]
MatrixForm[A]
aa = Length[A];
Print["First step in matrix multiplication A times A"]
MatrixForm[
 Table[Flatten[
   Table[Table[
     StringJoin[{"(", ToString[A[[nn, k]]], ")", "\[CenterDot]", "(", 
       ToString[A[[k, n]]], ")", 
       If[k < aa, "+", If[n == aa, "", ","]]}], {k, 1, aa}], {n, 1, 
     aa}]], {nn, 1, aa}]]
Print["Multiply:"]
MatrixForm[
 Table[Flatten[
   Table[Table[
     StringJoin[{"(", ToString[A[[nn, k]]*A[[k, n]]], ")", 
       If[k < aa, " +", If[n == aa, "", ",   "]]}], {k, 1, aa}], {n, 
     1, aa}]], {nn, 1, aa}]]
Print["and add:"]
MatrixForm[A.A]
$\endgroup$
1
$\begingroup$

Not a symbolically pure method but it does the job if one accepts that the terms are prepended with an empty space "" and wrapped with two square brackets [ ].

A = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}};
B = Table[Table[""[A[[n, k]]], {k, 1, Length[A]}], {n, 1, Length[A]}];
TableForm[B.B]

step by step matrix multiplication

$\endgroup$
1
  • $\begingroup$ Matrix multiplication spelled out: A = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}; B = A; TableForm[ Table[Table[Sum[A[[n, i]]*B[[i, k]], {i, 1, Length[A]}], {k, 1, Length[A]}], {n, 1, Length[A]}]] $\endgroup$ – Mats Granvik Feb 14 at 9:13
1
$\begingroup$

One can get (more drawn out) steps with the WolframAlpha command:

WolframAlpha["{{1,2,3},{4,5,6},{7,8,9}}.{{1,2,3},{4,5,6},{7,8,9}}", 
  {{"Result", 2}, "Content"}, PodStates -> {"Result__Step-by-step solution"}]

enter image description here

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.