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For my thesis in neural networks, I was trying to find a way to generalize a Sobel operator. I quickly thought of this: $$ \begin{bmatrix} a&b&c\\ d&0&-d\\ -c&-b&-a \end{bmatrix} $$ For example here is a quick list of different Sobel operators: $$ \begin{matrix} & a & b & c & d \\ \text{Vertical Sobel}\hfill & 1 & 2 & 1 & 0 \\ \text{Horizontal Sobel}\hfill & 1 & 0 & -1 & 2 \\ \text{Diagonal Sobel}\hfill & 2 & 1 & 0 & 1 \\ \text{Anti-Diagonal Sobel}\hfill & 0 & 1 & 2 & -1 \\ \end{matrix} $$ I wanted to give a name to this kind of matrix so that I can reference it later throughout my thesis. I was thinking of calling them antisymmetric, but I've seen that that term is also used for skew-symmetric matrices. What would you call them? derivative matrices? general Sobel matrices?

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    $\begingroup$ These are called "skew-centrosymmetric" matrices. Googling brings up some references. $\endgroup$ May 24, 2021 at 13:14
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    $\begingroup$ What a fast answer, thanks! If you post it as an answer I'll mark it as solved. $\endgroup$ May 24, 2021 at 13:17

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These are called "skew-centrosymmetric" matrices. The term "centrosymmetric matrix" seems to be popular enough to have its own Wikipedia page: https://en.wikipedia.org/wiki/Centrosymmetric_matrix

References on the skew version of these matrices can be found by Googling.

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