Accession Number : AD0742904

Title :   On the Solutions of the Matrix Equation XAX-X.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Greville,T. N. E.

Report Date : DEC 1971

Pagination or Media Count : 9

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)

Descriptors :   (*MATRICES(MATHEMATICS), THEOREMS), VECTOR SPACES

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE