EP Operators and Generalized Inverses

1975/08/01 by Stephen L. Campbell, Carl D. Meyer · 4 citations
Computer Science · Physics and Astronomy · Mathematics · #Matrix Theory and Algorithms #Electromagnetic Scattering and Analysis #Advanced Optimization Algorithms Research

paper · pdf · doi:10.4153/cmb-1975-061-4

Abstract

Abstract The relationship between properties of the generalized inverse of A, A† , and of the adjoint of A, A* , are studied. The property that A†A and AA† commute, called (E4), is investigated. (E4) generalizes the property of A being EP r . A canonical form and a formula for A† are given if a matrix A is (E4). Results are in a Hilbert space setting whenever possible. Examples are given.

Cited by

• Rank Equalities Related to Generalized Inverses of Matrices and Their Applications
• Fuglede-Putnam type commutativity theorems for EP operators
• Factorizations of EP operators
• Secondary range symmetric matrices. [europepmc]

Related

• Extending EP matrices by means of recent generalized inverses
• Properties of m -EP operators
• Characterizations of k-commutative equalities for some outer generalized inverses
• Further characterizations of the CMP inverse of matrices
• On a new generalized inverse of matrices