Rank and dimension functions

Manjunatha Prasad Karantha, Nupur Nandini, Divya P. Divya Shenoy

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Abstract

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.

Original languageEnglish
Article number11
Pages (from-to)144-155
Number of pages12
JournalElectronic Journal of Linear Algebra
Volume29
Issue number1
DOIs
Publication statusPublished - 22-10-2015

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All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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