Characterizations of <i>k</i>-commutative equalities for some outer generalized inverses

2018/07/26 by D. E. Ferreyra, F. E. Levis, F‎. ‎E‎. Levis +2 · 3 citations
Computer Science · Engineering · #Matrix Theory and Algorithms #Stability and Control of Uncertain Systems #Control Systems and Identification

paper · doi:10.1080/03081087.2018.1500994

Abstract

In this paper, we present necessary and sufficient conditions for the k-commutative equality AkX=XAk, where X is an outer generalized inverse of the square matrix A. Also, we give new representations for core EP, DMP, and CMP inverses of square matrices as outer inverses with prescribed null space and range. In addition, we characterize the core EP inverse as the solution of a new system of matrix equations.

Citations

• Core inverse of matrices
• Characterizations of the core inverse and the core partial ordering
• Core–EP inverse
• The class of<i>m</i>-<i>EP</i>and<i>m</i>-normal matrices
• On a new generalized inverse of matrices

Cited by

• Common properties among various generalized inverses and constrained binary relations
• New characterizations of weak CMP inverses
• Additive properties and absorption laws for generalized inverses

Related

• Further characterizations of the CMP inverse of matrices
• Extending EP matrices by means of recent generalized inverses
• EP Operators and Generalized Inverses
• On a new generalized inverse of matrices
• Core–EP inverse