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2005•Journal of Hunan University of Science and EngineeringRequires access

The Skew-Symmetric Solution of the Linear Matrix Equation(A~TXA, B~TXB)=(C,D)On The Linear Manifold

LI Zhen-zhu

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Abstract

Using the guotient singular value decomposition(QSVD)of a matrix pair,this paper obtaines the necessary and sufficient conditions for the existence of and the expressions for the skew-symmetric solution and for the least-squares skew-symmetric solution of the linear matrix equation(A~TXA,B~TXB)=(C,D)on the linear manifold.

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What this paper is about

Using the guotient singular value decomposition(QSVD)of a matrix pair,this paper obtaines the necessary and sufficient conditions for the existence of and the expressions for the skew-symmetric solution and for the least-squares skew-symmetric solution of the linear matrix equation(A~TXA,B~TXB)=(C,D)on the linear manifold.

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Available abstract

Using the guotient singular value decomposition(QSVD)of a matrix pair,this paper obtaines the necessary and sufficient conditions for the existence of and the expressions for the skew-symmetric solution and for the least-squares skew-symmetric solution of the linear matrix equation(A~TXA,B~TXB)=(C,D)on the linear manifold.

Key concepts: Skew-symmetric matrix, Mathematics, Matrix (chemical analysis), Symmetric matrix, Singular value decomposition, Skew, Manifold (fluid mechanics), Mathematical analysis

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