The Moore-Penrose inverse in rings with involution
Sanzhang Xu, Jianlong Chen
TL;DR
This paper explores conditions for the existence of the Moore-Penrose inverse in rings with involution and provides explicit formulas for computing it.
Contribution
It introduces new necessary and sufficient conditions for the Moore-Penrose inverse in rings with involution and derives explicit formulas for its computation.
Findings
New criteria for existence of Moore-Penrose inverse
Explicit formulas for the Moore-Penrose inverse
Enhanced understanding of ring elements with involution
Abstract
Let be a unital ring with involution.In this paper, several new necessary and sufficient conditions for the existence of the Moore-Penrose inverse of an element in a ring are given.In addition, the formulae of the Moore-Penrose inverse of an element in a ring are presented.
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Taxonomy
TopicsMatrix Theory and Algorithms · Advanced Topics in Algebra · graph theory and CDMA systems