The Least Squares {P,Q,k+1}-Reflexive Solution to a Matrix Equation  

矩阵方程的最小二乘{P,Q,k+1}-自反解

作　　者：DONG Chang-zhou LI Hao-xue 董昌州;李浩雪(School of Mathematics and Science,Hebei GEO University,Shijiazhuang 050031,China)

机构地区：[1]School of Mathematics and Science,Hebei GEO University,Shijiazhuang 050031,China

出　　处：《Chinese Quarterly Journal of Mathematics》2023年第2期210-220,共11页数学季刊(英文版)

基　　金：Supported by the Education Department Foundation of Hebei Province(Grant No.QN2015218).

摘　　要：Let P∈C^(m×m)and Q∈C^(n×n)be Hermitian and{k+1}-potent matrices,i.e.,P k+1=P=P∗,Qk+1=Q=Q∗,where(·)∗stands for the conjugate transpose of a matrix.A matrix X∈C m×n is called{P,Q,k+1}-reflexive(anti-reflexive)if P XQ=X(P XQ=−X).In this paper,the least squares solution of the matrix equation AXB=C subject to{P,Q,k+1}-reflexive and anti-reflexive constraints are studied by converting into two simpler cases:k=1 and k=2.

关 键 词：Matrix equations Potent matrix {P Q k+1}-reflexive(anti-reflexive) Canonical correlation decomposition Least squares solution 

分 类 号：O151.2[理学—数学]