TY - JOUR
T1 - Rank and dimension functions
AU - Karantha, Manjunatha Prasad
AU - Nandini, Nupur
AU - Divya Shenoy, Divya P.
N1 - Publisher Copyright:
© 2015, Electronic Journal of Linear Algebra. All Rights Reserved.
PY - 2015/10/22
Y1 - 2015/10/22
N2 - 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.
AB - 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.
UR - https://www.scopus.com/pages/publications/84981165506
UR - https://www.scopus.com/inward/citedby.url?scp=84981165506&partnerID=8YFLogxK
U2 - 10.13001/1081-3810.2999
DO - 10.13001/1081-3810.2999
M3 - Article
AN - SCOPUS:84981165506
SN - 1081-3810
VL - 29
SP - 144
EP - 155
JO - Electronic Journal of Linear Algebra
JF - Electronic Journal of Linear Algebra
IS - 1
M1 - 11
ER -