On the Solutions of the Matrix Equation XAX-X.
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WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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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
- Theoretical Mathematics