Classroom Note: Some Eigenvalue Properties of Persymmetric Matrices

Abstract

A matrix is called persymmetric (Golub and Van Loan, Matrix Computations, The Johns Hopkins University Press, 1989) if it is symmetric across its lower-left to upper-right diagonal, with similar definitions for per-antisymmetric and per-Hermitian matrices. This note shows some useful eigenvalue and eigenvector properties of matrices with two symmetries, such as matrices which are symmetric and persymmetric.