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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Factorization of singular matrices

Authors: A. R. Sourour and Kunikyo Tang
Journal: Proc. Amer. Math. Soc. 116 (1992), 629-634
MSC: Primary 15A23; Secondary 15A18
MathSciNet review: 1097352
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Abstract: We give a necessary and sufficient condition that a singular square matrix $ A$ over an arbitrary field can be written as a product of two matrices with prescribed eigenvalues. Except when $ A$ is a $ 2 \times 2$ nonzero nilpotent, the condition is that the number of zeros among the eigenvalues of the factors is not less than the nullity of $ A$. We use this result to prove results about products of hermitian and positive semidefinite matrices simplifying and strengthening some known results.

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