The Rank-constrained Symmetric Anti-reflexive Solution of a Linear Matrix Equation and its Approximation

Qingfeng XIAO

doi:10.12184/taposatWSP2633-456906.20200101

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The Rank-constrained Symmetric Anti-reflexive Solution of a Linear Matrix Equation and its Approximation

Volume 1, Issue 1

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The Rank-constrained Symmetric Anti-reflexive Solution of a Linear Matrix Equation and its Approximation
The Rank-constrained Symmetric Anti-reflexive Solution of a Linear Matrix Equation and its Approximation
Dongguan Polytechnic
Vol. 1, Issue 1, Pages: 36-43(2020)
DOI：10.12184/taposatWSP2633-456906.20200101
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QINGFENG XIAO. (2020). The Rank-constrained Symmetric Anti-reflexive Solution of a Linear Matrix Equation and its Approximation. Theory and Practice of Science and Technology, 1(1), 36-43..
DOI：

QINGFENG XIAO. (2020). The Rank-constrained Symmetric Anti-reflexive Solution of a Linear Matrix Equation and its Approximation. Theory and Practice of Science and Technology, 1(1), 36-43.. DOI： 10.12184/taposatWSP2633-456906.20200101.

摘要

Abstract

In this paper

the solvability conditions and the explicit expressions of the rankconstrained symmetric antireflexive solution of the matrix equation AX=B are established. Then the explicit expressions of the symmetric antireflexive minimal rank solutions are derived. The solutions of the corresponding optimal approximation problem for the symmetric antireflexive minimal rank solution matrices are also derived.

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Keywords

Matrix equationSymmetric anti-reflexive matrixMinimal rankOptimal approximate

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The Anti-Hermitian R-symmetric Extremal Rank Solutions of a Linear Matrix Equation

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