Rank and Dimension Functions

Prasad, Manjunatha K and Nandini, Nupur (2015) Rank and Dimension Functions. Electronic Journal of Linear Algebra, 29. pp. 144-155. ISSN 1081-3810

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In this paper, we invoke the theory of generalized inverses and the minus partial order on the study of regular matrices over a commutative ring to define rank–function for regular matrices and dimension–function 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.

Item Type: Article
Uncontrolled Keywords: Generalized inverse; Minus partial order; Matrices over commutative ring; Projective module; Rank– function; Dimension–function
Subjects: Departments at MU > Statistics
Depositing User: KMC Library
Date Deposited: 18 Dec 2015 09:07
Last Modified: 18 Dec 2015 09:07
URI: http://eprints.manipal.edu/id/eprint/144861

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