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

CAO Nan-bin, ZHANG Yu-ping

doi:10.13371/j.cnki.chin.q.j.m.2018.01.004

Chinese Quarterly Journal of Mathematics >

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

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

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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Abstract

Let P ∈ C^n×n be a Hermitian and {k + 1}-potent matrix, i.e., P^k+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

Cite this article

CAO Nan-bin, ZHANG Yu-ping . The {P; k + 1}-reflexive Solution to System of Matrix Equations AX = C; XB = D[J]. Chinese Quarterly Journal of Mathematics, 2018 , 33(1) : 32 -42 . DOI: 10.13371/j.cnki.chin.q.j.m.2018.01.004

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