2008•College MathematicsRequires access

The Centro-symmetric Solutions of Matrix Equation A~TXA=B on the Linear Manifold

LI Zhen-zhu

Abstract

Using the quotient singular value decomposition(QSVD) of matrix pairs, the necessary and sufficient conditions for the existence and the expressions for the centro-symmetric solutions of matrix equation ATXA=B on the linear manifold are established. In addition, in the solution set of corresponding equation, the expression of the optimal approximation solution to given matrix is derived.

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Key concepts: Mathematics, Symmetric matrix, Quotient, Matrix (chemical analysis), Manifold (fluid mechanics), Singular value decomposition, Centrosymmetric matrix, Mathematical analysis