The inverse problem of bisymmetric matrices with a submatrix constraint
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Abstract
Abstract An n × n real matrix A is called a bisymmetric matrix if A = A T and A = S n AS n , where S n is an n × n reverse unit matrix. This paper is mainly concerned with solving the following two problems: Problem I Given n × m real matrices X and B , and an r × r real symmetric matrix A 0 , find an n × n bisymmetric matrix A such that where A ([1: r ]) is a r × r leading principal submatrix of the matrix A . Problem II Given an n × n real matrix A * , find an n × n matrix  in S E such that where ∥·∥ is Frobenius norm, and S E is the solution set of Problem I. The necessary and sufficient conditions for the existence of and the expressions for the general solutions of Problem I are given. The explicit solution, a numerical algorithm and a numerical example to Problem II are provided. Copyright © 2003 John Wiley & Sons, Ltd.