Abstract
AbstractAn n×n real matrix A is called a bisymmetric matrix if A=AT and A=SnASn, where Sn is an n×n reverse unit matrix. This paper is mainly concerned with solving the following two problems:Problem IGiven n×m real matrices X and B, and an r×r real symmetric matrix A0, 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 IIGiven an n×n real matrix A*, find an n×n matrix  in SE such that where ∥·∥ is Frobenius norm, and SE 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.
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