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On Solutions of Matrix Equation $AXA^T+BYB^T=C$

On Solutions of Matrix Equation $AXA^T+BYB^T=C$

Year:    2005

Journal of Computational Mathematics, Vol. 23 (2005), Iss. 1 : pp. 17–26

Abstract

By making use of the quotient singular value decomposition (QSVD) of a matrix pair, this paper establishes the necessary and sufficient conditions for the existence of and the expressions for the general solutions of the linear matrix equation $AXA^T+BYB^T=C$ with the unknown $X$ and $Y$, which may be both symmetric, skew-symmetric, nonnegative definite , positive definite or some cross combinations respectively. Also, the solutions of some optimal problems are derived.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2005-JCM-8792

Journal of Computational Mathematics, Vol. 23 (2005), Iss. 1 : pp. 17–26

Published online:    2005-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    10

Keywords:    Matrix equation Matrix norm QSVD Constrained condition Optimal problem.