Say, I have two matrices $A_1$ and $A_2$, what is a good way to check how similar they are...
There have been questions asked before, and the answer suggest Froberius norm, for example. But Frobenium norm only gives you 1 number, and hence fails to say which part of the matrices are closed and which are not.
This suggests the use of comparing the matrices singular values/eigenvalues. The drawback is then you can't tell anything about singular vectors/eigenvectors.
So would a good comparision be 1) Frobenius norm 2) Singular/Eigen Values and (3) Singular/Eigenvectors? Would that be a little bit too much?
