A Rao-regular matrix and the Rao idempotent of a matrix over a commutative ring are defined. We prove that a matrix A over a commutative ring is regular if and only if A is a sum of Rao-regular matrices with mutually orthogonal Rao idempotents. We find necessary and sufficient conditions for a matrix to have group inverse over a commutative ring. Also, we give a method for computing minors of reflexive g-inverse whenever it exists.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Numerical Analysis