antidiagonal matrix
Let $A$ be a square matrix^{} (over any field $\mathbb{F}$). An entry in $A$ is an antidiagonal entry if it is on the line going from the lower left corner of $A$ to the upper right corner. If all entries in $A$ are zero except on the antidiagonal, then $A$ is an antidiagonal matrix.
If ${a}_{1},\mathrm{\dots},{a}_{n}\in \mathbb{F}$, let
$$\mathrm{adiag}({a}_{1},\mathrm{\dots},{a}_{n})=\left(\begin{array}{ccccc}\hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill {a}_{1}\hfill \\ \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill {a}_{2}\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 0\hfill & \hfill {a}_{3}\hfill & \hfill \hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill \cdot \hfill & \hfill 0\hfill & \hfill \hfill & \hfill 0\hfill \\ \hfill {a}_{n}\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill \hfill & \hfill 0\hfill \end{array}\right).$$ 
Properties of antidiagonal matrices

1.
If $A$ and $D$ are $n\times n$ antidiagonal and diagonal matrices^{}, respectively, then $AD,DA$ are antidiagonal.

2.
The product of two antidiagonal matrices is an diagonal matrix.
Title  antidiagonal matrix 

Canonical name  AntidiagonalMatrix 
Date of creation  20130322 15:12:20 
Last modified on  20130322 15:12:20 
Owner  matte (1858) 
Last modified by  matte (1858) 
Numerical id  8 
Author  matte (1858) 
Entry type  Definition 
Classification  msc 1500 