数学季刊 >

2018 , Vol. 33 >Issue 1: 32 - 42

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2018.01.004

矩阵方程组AX=C;XB=D{P;k+1}-反射解的研究

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  • 1. Collage of Mathematics and Information Science, Hebei Normal University2. School of Mathematics and Science, Hebei GEO University
ZHANG Yu-ping(1982-), male, native of Shijiazhuang, Hebei, an associate professor of Shijiazhuang University of Economics, M.S.D., engages in matrix algebra.

收稿日期: 2015-06-03

  网络出版日期: 2020-10-09

基金资助

Supported by the Education Department Foundation of Hebei Province(QN2015218)； Supported by the Natural Science Foundation of Hebei Province(A2015403050)；

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The {P; k + 1}-reflexive Solution to System of Matrix Equations AX = C; XB = D

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  • 1. Collage of Mathematics and Information Science, Hebei Normal University2. School of Mathematics and Science, Hebei GEO University
ZHANG Yu-ping(1982-), male, native of Shijiazhuang, Hebei, an associate professor of Shijiazhuang University of Economics, M.S.D., engages in matrix algebra.

Received date: 2015-06-03

  Online published: 2020-10-09

Supported by

Supported by the Education Department Foundation of Hebei Province(QN2015218)； Supported by the Natural Science Foundation of Hebei Province(A2015403050)；

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摘要

Let P ∈ Cn×n be a Hermitian and {k + 1}-potent matrix, i.e., Pk+1= P = P*,where（·）*stands for the conjugate transpose of a matrix. A matrix X ∈ Cn×nis called{P, k + 1}-reflexive（anti-reflexive） if PXP = X（P XP =-X）. The system of matrix equations AX = C, XB = D subject to {P, k + 1}-reflexive and anti-reflexive constraints are studied by converting into two simpler cases: k = 1 and k = 2, the least squares solution and the associated optimal approximation problem are also considered.

关键词： system of matrix equations; potent matrix; {P; k+1}-reflexive (anti-reflexive); approximation problem; least squares solution

本文引用格式

曹南斌, 张玉平 . 矩阵方程组AX=C;XB=D{P;k+1}-反射解的研究[J]. 数学季刊, 2018 , 33(1) : 32 -42 . DOI: 10.13371/j.cnki.chin.q.j.m.2018.01.004

Abstract

Let P ∈ Cn×n be a Hermitian and {k + 1}-potent matrix, i.e., Pk+1= P = P*,where（·）*stands for the conjugate transpose of a matrix. A matrix X ∈ Cn×nis called{P, k + 1}-reflexive（anti-reflexive） if PXP = X（P XP =-X）. The system of matrix equations AX = C, XB = D subject to {P, k + 1}-reflexive and anti-reflexive constraints are studied by converting into two simpler cases: k = 1 and k = 2, the least squares solution and the associated optimal approximation problem are also considered.

Key words： system of matrix equations; potent matrix; {P; k+1}-reflexive (anti-reflexive); approximation problem; least squares solution

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