# 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

# Descriptors:

# Subject Categories:

- Theoretical Mathematics