I have a matrix that I obtained from theoretical computation and I have another matrix which I obtained by actual data collection. How do I compare the two matrices? How do I state that one matrix is significantly different from the other?
I have looked into:
- Frobenius Norm but I don't know what should be my threshold for comparison.
- Looking at max and min deviation of one matrix from the other. But again, what's a good threshold?
I thought that to say one matrix varies significantly from the other, I would need to quantify the variance of those terms and compare how the deviation compares to the variance (or SD) but sadly, I don't have data for that and neither can I theoretically estimate any variances.
I am kind of lost in what would be a good metric.