TY - JOUR
T1 - Generalized inverses over integral domains. II. group inverses and Drazin inverses
AU - Manjunatha Prasad, K.
AU - Bhaskara Rao, K. P S
AU - Bapat, R. B.
PY - 1991/2/15
Y1 - 1991/2/15
N2 - This is a continuation of an earlier paper by the authors on generalized inverses over integral domains. The main results consist of necessary and sufficient conditions for the existence of a group inverse, a new formula for a group inverse when it exists, and necessary and sufficient conditions for the existence of a Drazin inverse. We show that a square matrix A of rank r over an integral domain R has a group inverse if and only if the sum of all r × r principal minors of A is an invertible element of R. We also show that the group inverse of A when it exists is a polynomial in A with coefficients from R.
AB - This is a continuation of an earlier paper by the authors on generalized inverses over integral domains. The main results consist of necessary and sufficient conditions for the existence of a group inverse, a new formula for a group inverse when it exists, and necessary and sufficient conditions for the existence of a Drazin inverse. We show that a square matrix A of rank r over an integral domain R has a group inverse if and only if the sum of all r × r principal minors of A is an invertible element of R. We also show that the group inverse of A when it exists is a polynomial in A with coefficients from R.
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U2 - 10.1016/0024-3795(91)90018-R
DO - 10.1016/0024-3795(91)90018-R
M3 - Article
AN - SCOPUS:0039429209
SN - 0024-3795
VL - 146
SP - 31
EP - 47
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
IS - C
ER -