Suppose I have two matrices $\textbf{A}$, and $\textbf{B}$ as follows:

$\begin{array}{c=c} \textbf{A} = \left[ \begin{array}{ccc} a_{11} & a_{12} & a_{13}\\ a_{21} & a_{22} & a_{23}\\ a_{31} & a_{32} & a_{33}\\ \end{array}\right] \end{array}$ , and $\begin{array}{c=c} \textbf{B} = \left[ \begin{array}{ccc} b_{11} & b_{12} & b_{13}\\ b_{21} & b_{22} & b_{23}\\ b_{31} & b_{32} & b_{33}\\ \end{array}\right] \end{array}$

I am looking for a way to write, in matrix language, this operation:


The matrices can be rectangular in such a way that $\textbf{A}$ can of mxn dimension and $\textbf{B}$ can be of nxm dimension. If this is possible, I would be grateful for a clue.



if $C = A B$ is the matrix product, then the elements are $c_{i,j} = \sum_k a_{i,k} b_{k,j}$. Then the trace of $C$ will be

$Tr(C) = \sum_k c_{k,k} = \sum_k \Big( \sum_l a_{k,l}b_{l,k}\Big)$

which seems to be what you are looking for.

  • $\begingroup$ @ Yul Otani. This is what I was looking for. Thanks. $\endgroup$ – Celdor Jun 11 '13 at 18:13

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.