Diagonal of a matrix in different basis

Question

I want to calculate the diagonal of a matrix in different basis $V' A V$ where $V$ is the unitary matrix and $A$ is the matrix. What is the least computational expensive way?

If I calculate $V' A V$ and throw away all elements other than diagonal, it would be inefficient. I am using Matlab.

score 1 · Accepted Answer · answered Mar 19 '14 at 22:03

1

Assuming real matrices, $$ (V'AV)_{kk}=\sum_{s,t}A_{st}V_{sk}{V_{tk}} $$

answered Mar 19 '14 at 22:03

Martin Argerami

205,756

Thanks, do you know a shortcut in matlab to avoid the loop? – Roy Mar 19 '14 at 22:21
Sorry, I have no experience with Matlab. But there is not way to avoid adding all the terms, unless in the case of a very particular form of matrix (like diagonal, etc.) – Martin Argerami Mar 19 '14 at 22:34

Diagonal of a matrix in different basis

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