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2012•Journal of Chongqing Technology and Business UniversityRequires access

The Moore-Penrose Inverse for Generalized Row(Column)Symmetric Matrix

Wei Guo

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Abstract

The concept of generalized row(column)symmetric matrix is given,its full rank decomposition and singular value decomposition are studied.By the two decompositions and orthogonal equivalence,three shortcut counting methods of the Moore-Penrose inverse for generalized row(column)symmetric matrix are obtained,which can dramatically reduce the amount of calculation and save the CPU time and memory,which extend the results of the related references and which spread its application scope.

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What this paper is about

The concept of generalized row(column)symmetric matrix is given,its full rank decomposition and singular value decomposition are studied.By the two decompositions and orthogonal equivalence,three shortcut counting methods of the Moore-Penrose inverse for generalized row(column)symmetric matrix are obtained,which can dramatically reduce the amount of calculation and save the CPU time and memory,which extend the results of the related references and which spread its application scope.

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Available abstract

The concept of generalized row(column)symmetric matrix is given,its full rank decomposition and singular value decomposition are studied.By the two decompositions and orthogonal equivalence,three shortcut counting methods of the Moore-Penrose inverse for generalized row(column)symmetric matrix are obtained,which can dramatically reduce the amount of calculation and save the CPU time and memory,which extend the results of the related references and which spread its application scope.

Key concepts: Column (typography), Singular value decomposition, Inverse, Mathematics, Matrix (chemical analysis), Equivalence (formal languages), Rank (graph theory), Moore–Penrose pseudoinverse

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