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《Journal of Jilin University (Science Edition)》 2005-04
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On Moore-Penrose Inverses of Matrices over a Ring

CEN Jian-miao(Department of Mathematics, Ningbo University, Ningbo 315211, Zhejiang Province, China)  
The Moore-Penrose inverses of matrices over a ring R with an involution * and unitary are (discussed). Some necessary and sufficient conditions for the existence of the Moore-Penrose inverse of matrices over a ring R are given. In particular, it is obtained that a necessary and sufficient condition for the existence of the Moore-Penrose inverse of a matrix A over a ring R is that A=GDH, where D~2=D=D~*,( (GD)~*GD+I-D ) and (DH(DH)~*+I-D) are invertible.
【Fund】: 浙江省自然科学基金(批准号:102066).
【CateGory Index】: O241.6
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