I have a matrix
A which is an approximation to the known matrix
B. Both matrices are square, 3x3 matrices and, in this case, are symmetric. Is there a 'best' method for calculating percent error in the approximation? I had been using the sum the 'sum of squares' error for all entries divided by the sum of 'sum of squares' of the true matrix,
pct_err = sum(sum( (A-B).^2 ))/(sum(sum(B.^2))
and realized that this is simply the square of
norm(A-B,2)/norm(B,2) which gives drastically different percent error estimates.
How should I go about calculating percent error between two matrices, or maybe more generally, two tensors?
EDIT: Thanks to some of the comments, I now recognize the difference between the 2-norm and the Frobenius norm. In either case, however, the type of norm I am taking is of relatively small consequence. The bigger question is how to represent the percent error of a 2nd rank tensor correctly.