Divergence matrix interpretation and linear combination

Question

Paola 2019-8-16

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https://ww2.mathworks.cn/matlabcentral/answers/476361-divergence-matrix-interpretation-and-linear-combination

Hello,

I am new to the mathematical concept of divergence, even if it is quite clear to understand it in figures or examples.

I have calculated the divergence of different matrices (representig Factors extracted froma data matrix using Gradient Descent, namely I have 5 of them).

I used the matlab function div=divergence (X,Y,U,V), where X and Y are 4x4 coordinates matrices and U and V the corresponding 4x4 matrices of the data.

As result, I got several 4x4 divergence matrix, (for each factor), that are composed by mainly positive values.

1) It is not really clear to me how this matrix gives me info about the divergenge of the data:

given that most of the elements in the divergence matrix are positive and
the mean (y = nanmean(Div,'all')) returns a positive number
Does this mean that the Factor is divergent?

2) I would need to combine all the different factors (e.g. 1 and 2, 2 and 4, etc) in order to test if the divergence matrix of their linear combination confirms the result of the one obtained on a single factor (e.g. if the Div matrix on the single factor is divergent, the div matrix on the linear combination of different matrices, is still divergent or will become congergent?)

Thank you!