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On Generalized Inverses of A Block in A Partitioned Matrix

Liu Gui-xiang

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Abstract

Let M=AX X is real symmetric matrix, X is of full column rank,and G=[JB(HL2BY Y′]D[HL[JB) is real symmetric matrix.In this paper,we give the conditions that B is the g inverse,reflexive inverse and Moore Penrose inverse of A ,and obtain for mula for the corresponding generalized inverses of A . [WTHZ]

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Let M=AX X is real symmetric matrix, X is of full column rank,and G=[JB(HL2BY Y′]D[HL[JB) is real symmetric matrix.In this paper,we give the conditions that B is the g inverse,reflexive inverse and Moore Penrose inverse of A ,and obtain for mula for the corresponding generalized inverses of A . [WTHZ]

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Available abstract

Let M=AX X is real symmetric matrix, X is of full column rank,and G=[JB(HL2BY Y′]D[HL[JB) is real symmetric matrix.In this paper,we give the conditions that B is the g inverse,reflexive inverse and Moore Penrose inverse of A ,and obtain for mula for the corresponding generalized inverses of A . [WTHZ]

Key concepts: Inverse, Mathematics, Matrix (chemical analysis), Rank (graph theory), Generalized inverse, Block (permutation group theory), Combinatorics, Moore–Penrose pseudoinverse

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