# "How much diagonal" a matrix is

I have a (biological) computational system that outputs squared matrices. These matrices will sometimes have a tendency to be diagonal-like, with higher values at and around the diagonal.

I would like to have some summary measure on how "much diagonal" a matrix is, so that I can batch process hundreds of outputs and score them on how much the higher entries cluster in and around the diagonal.

Any ideas of some standard approach that I can generalise?

Thanks ! JL

$\sum_i((A[i,i])^2) \over \epsilon + \sum_{i \ne j}((A[i,j])^2)$