Hello, I have two n*n correlation matrices with values ranging between -1,1. (2 correlation matrix because I have the same n terms under 2 different conditions) I then transformed the correlation into a similarity matrix where values range between [0,1]. The similarity was computed using the formula here: http://genomebiology.com/content/inline/gb-2007-8-7-r149-i2.gif where lij = summation(aiu.auj) and aiu= is correlation value between ith and uth element in the correlation matrix. ki,kj in our case is n-1.

This gives me 2 similarity matrices.

My question is how can I compute the difference between the similarity matrices (SIM)? Will doing a simple abs(SIM1-SIM2) make statistical/mathematical sense? Is there a robust way to find/quantify difference between two similarity matrices?

Any ideas will be truly appreciated. Thanks in advance.