Rank and dimension functions

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

Research output: Contribution to journalArticle

1 Citation (Scopus)

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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Dimension Function
Dimension of a vector space
Projective Module
Generalized Inverse
Partial Order
Commutative Ring
Finitely Generated
Rank of a matrix
Module
Theorem

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

Karantha, Manjunatha Prasad ; Nandini, Nupur ; Divya Shenoy, Divya P. / Rank and dimension functions. In: Electronic Journal of Linear Algebra. 2015 ; Vol. 29, No. 1. pp. 144-155.
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Karantha, MP, Nandini, N & Divya Shenoy, DP 2015, 'Rank and dimension functions', Electronic Journal of Linear Algebra, vol. 29, no. 1, 11, pp. 144-155. https://doi.org/10.13001/1081-3810.2999

Rank and dimension functions. / Karantha, Manjunatha Prasad; Nandini, Nupur; Divya Shenoy, Divya P.

In: Electronic Journal of Linear Algebra, Vol. 29, No. 1, 11, 22.10.2015, p. 144-155.

Research output: Contribution to journalArticle

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