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):

Report Date:

1971-12-01

Pagination or Media Count:

9.0

Abstract:

For a given m x n complex matrix A, it is shown that X satisfies XAXX 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

Subject Categories:

  • Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE