How does one establish matrix similarity in a metrical fashion? Suppose one wants a distance metric that describes the information necessary to convert one matrix into another.  How would one go about doing it?
The first thing that I tried was literally that, but it does not seem to match the concept:
B A^{-1} = P

entropy = H(pseudoInverse(P))


The result was the following:

And:

It seems like what is going on is that I am getting an inverse among many possible inverses, and what I really want is some ideal transform that is able to, as conservatively as possible, convert one item into the other.
Ideally, the entropy is lower for the X than the __.  Is there a straightforward way to get this similarity metric?

Right now my thinking is that instead of the literal images above, I should construct some sort of ordered adjacency matrix of pixels.
Then, I should compute the SVD and discover whether the projection of the adjacency matrix onto the SVD components is close or far...
(At least, it is something I'll try).

Found this idea called the 'Homography Matrix', and I think there might be a thread to pull on there:
How to align images using OpenCV
