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

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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!
  4 Comments
dpb
dpb on 2 Oct 2022
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.

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