Linear Algebra Question

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scottw

Posted: Mon May 21, 2007 9:29 pm

Guest

I know that:

\sum_{i,j} A_{i,j} * B_{i,j} = \sum_{i,j} A_{i,j} * B^T_{j,j} =
\sum_{i} (AB^T)_{ii} = trace(AB^T)

In Matlab this is sum(sum(A.*B)) = trace(A*B')

Can anyone tell me if there is a way to similar way to reduce the
expression :

\sum_{i,j} A_{i,j} * B_{i,j} * C_{i,j}

so that element-wise multiplication of the corresponding (i,j) cells
across each matrix is not required, e.g. using the properties of the
trace somehow?

thanks,
Scott

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