Rank and dimension functions
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In this paper, we invoke theory of generalized inverses and minus partial order on regular matrices over a commutative ring to define rankâfunction for regular matrices and dimensionâfunction for finitely generated projective modules which are direct summands of a free module. Some properties held by the rank of a matrix and the dimension of a vector space over a field are generalized. Also, a generalization of rank-nullity theorem has been established when the matrix given is regular.
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