Should I use mantel test to test for signifance between [nxm] matrices?

I was looking into the Mantel test, but I'm worried that I was going to get myself into a pitfall.

I read that it would be erronous to use a mantel test for datasets spatial auto-correlation, and I'm not sure if my dataset (I've included an image) falls into this category.

Essetially, what I'm trying to do is to decompose my matrix into vectors which I can multiply together to retrive an analog to the 2d matrix. I want to apply a test to show that there is no significant difference between the original matrix and the matrix that I got from the vector multiplication.

Would the Mantel test show that, or would it be erronous? If so, what test should I apply to test for significance between matrices.

Thanks in advnace!

[Torsten]

I want to apply a test to show that there is no significant difference between the original matrix and the matrix that I got from the vector multiplication.

But that's in no way a situation for a statistical test because you don't get the comparison matrix empirically, but you deduce it from the original matrix by algebraic operations, don't you ? By the formulae on how you deduce the second matrix from the first, you can exactly quantify the correlation between the two matrices - you don't need to test for it.

[Fouad Azar]

I was worried that I was making that mistake. So, because I derived Modes A and B from the "Original Matrix" and used them to deduce the other matrix (ModeA.*ModeB ), I shouldn't apply a statistical test.

[Torsten]

Yes, you derived the second matrix from the original by algebraic operations. You didn't get it without knowledge how it was created. In my opinion, the latter were a situation for a statistical test, the first maybe for numerical optimization.

[dpb]

Agree w/ @Torsten; this is not a statistical test, but...since Mantel is an application of regression, I think you could use the computed statistic as a performance measure similar to the Pearson correlation; you just can't draw any statistical conclusions regarding the expected value. It, like Pearson, is an R of [-1 1]; one presumes essentially 1.0 will be the result if the reconstruction is good.