Persymmetric matrix

A persymmetric matrix, also known as a symmetric Toeplitz matrix, is a special type of square matrix that exhibits symmetry in a specific manner. An \( n \times n \) matrix \( A \) is defined as persymmetric if it satisfies the condition: \[ A[i, j] = A[n-j+1, n-i+1] \] for all valid indices \( i \) and \( j \).