Anti-diagonal matrix
In mathematics, an anti-diagonal matrix is a matrix where all the entries are zero except those on the anti-diagonal (the diagonal going from the lower left corner to the upper right corner).
More precisely, an n-by-n matrix A is an anti-diagonal matrix if the (i, j) element is zero for all i, j ∈ {1, …, n} with i + j ≠ n + 1.
An example of an anti-diagonal matrix is
All anti-diagonal matrices are also persymmetric.
The product of two anti-diagonal matrices is a diagonal matrix. Furthermore, the product of an anti-diagonal matrix with a diagonal matrix is anti-diagonal, as is the product of a diagonal matrix with an anti-diagonal matrix.