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?



Is there a name for this type of matrix?
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.


