The anti-symmetric ortho-symmetric solutions of the matrix equation A^TXA=D

Qing-Feng Xiao, Xi-Yan Hu, Lei Zhang
2009 The Electronic Journal of Linear Algebra  
In this paper, the following problems are discussed. Problem I. Given matrices A ∈ R n×m and D ∈ R m×m , find X ∈ ASR n P such that A T XA = D, where ASR n P = {X ∈ ASR n×n |P X ∈ SR n×n for given P ∈ OR n×n satisfying P T = P }. Problem II. Given a matrixX ∈ R n×n , findX ∈ S E such that where · is the Frobenius norm, and S E is the solution set of Problem I. Expressions for the general solution of Problem I are derived. Necessary and sufficient conditions for the solvability of Problem I are
more » ... y of Problem I are provided. For Problem II, an expression for the solution is given as well.
doi:10.13001/1081-3810.1291 fatcat:wfrmscchujapzk2rrweavjlcxi