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Commutation of several matrices using Do?

Nomsa Ledwaba

Posted 3 years ago

Hello Wolfram Community I have a list of lists. That is a matrix (listSym) containing matrices (A[1], A[2], .... , A[6]). A[1] = {{0, 0, 2, 0, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}}; A[2] = {{0, 0, 0, 1, 0, 0}, {0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}}; A[3] = {{0, 0, 2, 0, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}}; A[4] = {{0, 0, 0 , 1, 0, 0}, {0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}}; A[5] = {{0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 2, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}}; A[6] = {{0, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}}; listSym = {A[1], A[2], A[3], A[4], A[5], A[6]}; dim = Length[listSym]; The matrix commutation of A[5] with listSym is: AdjointMatrixCommutator [i_] := TableForm[ Dot[A[5], listSym[[i]]] - Dot[ listSym[[i]], A[5]], {i, 1, dim}, TableHeadings -> Automatic] I want to do a commutation of A[1] with listSym, A[2] with listSym, A[3] with listSym, etc. The matrix commutation of each A[i] with listSym (using a Do Loop) is: Do[Print[TableForm[ Dot[A[i], listSym[[i]]] - Dot[listSym[[i]], A[i]], {i, 1, dim}]], {i, 1, dim}]; I am getting matrices which are all zeros and that is incorrect. Can anyone show how to use a Do loop with lists (of matrix commutation). Ps: I can provide more information for a better answer.

Hello Wolfram Community

I have a list of lists. That is a matrix (listSym) containing matrices (A[1], A[2], .... , A[6]).

A[1] = {{0, 0, 2, 0, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}};
A[2] = {{0, 0, 0, 1, 0, 0}, {0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}};
A[3] = {{0, 0, 2, 0, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}};
A[4] = {{0, 0, 0 , 1, 0, 0}, {0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}};
A[5] = {{0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 2, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}};
A[6] = {{0, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}};
listSym = {A[1], A[2], A[3], A[4], A[5], A[6]};
dim = Length[listSym];

The matrix commutation of A[5] with listSym is:

AdjointMatrixCommutator [i_] :=  TableForm[ Dot[A[5], listSym[[i]]] - Dot[ listSym[[i]], A[5]], {i, 1, dim}, TableHeadings -> Automatic]

I want to do a commutation of A[1] with listSym, A[2] with listSym, A[3] with listSym, etc.

The matrix commutation of each A[i] with listSym (using a Do Loop) is:

Do[Print[TableForm[   Dot[A[i], listSym[[i]]] - Dot[listSym[[i]], A[i]], {i, 1, 
    dim}]], {i, 1, dim}];

I am getting matrices which are all zeros and that is incorrect. Can anyone show how to use a Do loop with lists (of matrix commutation).

Ps: I can provide more information for a better answer.

POSTED BY: Nomsa Ledwaba

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Rohit Namjoshi

Posted 3 years ago

`Dot` is commutative so this will always be zero. Dot[A[i], listSym[[i]]] - Dot[listSym[[i]], A[i]] Perhaps you meant Do[Print[ Table[ Dot[A[i], listSym[[j]]] - Dot[listSym[[j]], A[i]], {i, 1, dim}]], {j, 1, dim}]; Note that `TableForm`, as with most `Form` wrappers is not computable. The definition of `AdjointMatrixCommutator` should not use `TableForm`, use `Table` instead, and apply `TableForm` to the result if you want formatted output.

POSTED BY: Rohit Namjoshi

Nomsa Ledwaba

Posted 3 years ago

May I ask why listSym varies in this case, meaning why you used listSym[j], { j, 1, dim} instead of listSym only ?

POSTED BY: Nomsa Ledwaba

Nomsa Ledwaba

Posted 3 years ago

Yes indeed it is sorted. Thank you.

POSTED BY: Nomsa Ledwaba

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