Constructing and counting regular triangular matrices

ABSTRACT

Von Neumann regularity within a ring of upper triangular matrices is characterized in terms of how such a matrix and an upper triangular generalized inverse can be constructed. In the case of a finite ring, this yields a method for implicitly counting all upper triangular matrices that admit upper triangular generalized inverses.

Keywords:

• Von Neumann regular
• generalized inverse
• non-commutative ring
• finite ring

AMS CLASSIFICATIONS:

• 15A24c
• 15B33

Disclosure statement

No potential conflict of interest was reported by the author.