On the Solutions of the Matrix Equation XAX-X.

Abstract

For a given m x n complex matrix A, it is shown that X satisfies XAX=X if and only if it expressible in the form X = (EAF)*, where E and F are Hermitian idempotents and the * denotes the Moore-Penrose inverse. In particular, a matrix is idempotent if and only if it is the Moore-Penrose inverse of the product of two Hermitian idempotents. (The 'if' part of the latter statement was previously shown by Cline). (Author)

Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1971
Accession Number
AD0742904

Entities

People

  • Thomas N.E. Greville

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Equations

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.