# Is there a name for this type of matrix?

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?

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