I want to calculate the difference between two n x n matrices to a scaler. That measure should give the idea about the physical location of each values too. For example if I name some operation with '~'
A = 1 0 B = 2 0 C = 0 0 D = 0 0
0 0 0 0 1 0 2 0
If '~' is to compare each pixel which is A[i, j] with B[i, j] and to get the summation of them, it gives B ~ A = D ~ C = 1
But since the measure should give an idea about the locations B ~ A and D ~ C cannot be equal because in A,B the change is in [0,0] and in C,D the change is in [1,0]
So what are the measures/ ways that I can calculate the difference of two matrices to a scaler reflecting their physical locations?
For $A\sim B$ you could calculate a new matrix $N_{ij} = \left\{\begin{array}{l}1 \text{ if } A_{ij}\ne B_{ij}\\0 \text{ if } A_{ij}= B_{ij}\end{array}\right.$, then define $A \sim B = \displaystyle\sum_{i=1}^n\sum_{j=1}^n N_{ij}2^{in+j}$. Then $\sim$ is basically a large binary number, each non-zero bit of which indicates a difference between $A$ and $B$ at a particular location.