2008•Journal of Guangxi Academy of SciencesRequires access

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

LI Zhen-zhu

Abstract

By applying the generalized singular value decomposition of a matrix pair,the necessary and sufficient conditions and the expressions for the D-symmetric solutions of matrix equation ATXA=B on the linear manifold are established.In addition,the least-squares solutions of ATXA=B with respect to D-symmetric matrix are derived.

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Key concepts: Symmetric matrix, Matrix (chemical analysis), Singular value decomposition, Mathematics, Manifold (fluid mechanics), Centrosymmetric matrix, Pure mathematics, Decomposition