| In this paper, generalized inverses of matrix over communicative rings and its applications were studied:(1)The relationships are discussed between a matrix A and its bordered matrix over commutative rings in terms of subdeterminants. Necessary and sufficient conditions are given, for the existence of the Moore - Penrose inverse and the Drazin inverse of a matrix over commutative rings, by its bordered matrices. Representations of the group inverse and Drazin inverse are given in terms of subdeterminants. An algorithm for the generalized inverses was given over commutative rings.(2) The generalized Moore - Penrose inverse and Khatri - inverse were studied. Necessary and sufficient conditions for their existence over integral domains were given. Formulas were given in terms of subdeterminants. |
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