On Real Solutions of the Equation Φ^t (A) = 1/n J_n

Yuming Chen, Wilfrid Laurier University

This article was originally published in SIAM Journal on Matrix Analysis and Applications, 22(3): 965-970. © 2001 Society for Industrial and Applied Mathematics.

Abstract

For a class of n × n-matrices, we get related real solutions to the matrix equation Φ^t (A) = 1/n J_{n by generalizing the approach of and applying the results of Zhang, Yang, and Cao [SIAM J. Matrix Anal. Appl., 21 (1999), pp. 642–645]. These solutions contain not only those obtained by Zhang, Yang, and Cao but also some which are neither diagonally nor permutation equivalent to those obtained by Zhang, Yang, and Cao. Therefore, the open problem proposed by Zhang, Yang, and Cao in the cited paper is solved.}