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2013 Eigenvector-Free Solutions to the Matrix Equation AXBH=E with Two Special Constraints
Yuyang Qiu
J. Appl. Math. 2013: 1-7 (2013). DOI: 10.1155/2013/869705

Abstract

The matrix equation AXBH=E with SX=XR or PX=sXQ constraint is considered, where S, R are Hermitian idempotent, P, Q are Hermitian involutory, and s=±1. By the eigenvalue decompositions of S, R, the equation AXBH=E with SX=XR constraint is equivalently transformed to an unconstrained problem whose coefficient matrices contain the corresponding eigenvectors, with which the constrained solutions are constructed. The involved eigenvectors are released by Moore-Penrose generalized inverses, and the eigenvector-free formulas of the general solutions are presented. By choosing suitable matrices S, R, we also present the eigenvector-free formulas of the general solutions to the matrix equation AXBH=E with PX=sXQ constraint.

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Yuyang Qiu. "Eigenvector-Free Solutions to the Matrix Equation AXBH=E with Two Special Constraints." J. Appl. Math. 2013 1 - 7, 2013. https://doi.org/10.1155/2013/869705

Information

Published: 2013
First available in Project Euclid: 14 March 2014

zbMATH: 06950918
MathSciNet: MR3122124
Digital Object Identifier: 10.1155/2013/869705

Rights: Copyright © 2013 Hindawi

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