To expand upon the title, I am wondering if there is a specific name for square matrices of the form: $$M = \begin{bmatrix} a_{11} & 0 & \cdots & 0 & \cdots & & 0 & b_{1n} \\ 0 & a_{22} & 0 & \cdots & & b_{2 \ i} & & 0 \\ 0 & \ddots & \ddots & & \cdot^{\textstyle \cdot^{\textstyle \cdot}} & 0 & & 0 \\ & & & a_{} & & \vdots & & \\ \vdots & 0 & \cdot^{\textstyle \cdot^{\textstyle \cdot}} & 0 & \ddots & 0 & & \vdots\\ & \cdots & b_{i \ n-(i+1)} & \cdots & & a_{i \ i} &\\ 0 & \cdot^{{\textstyle \cdot}^{\textstyle \cdot}} & & & & \ddots & \ddots & 0\\ b_{n 1} & 0 & \cdots & 0 & & \cdots & & a_{nn} \end{bmatrix} \\$$ where, $ M = A_{\text{diagonal}} + B_{\text{anti-diagonal}}$ Essentially, M is a square matrix which is zero everywhere except the main and anti-diagonals. In other words, it is the sum of diagonal and anti-diagonal square matrices with the same dimension.

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