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

DOI:
https://doi.org/10.1090/S0002-9939-1992-1097352-4

MathSciNet review:
1097352

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Abstract: We give a necessary and sufficient condition that a singular square matrix over an arbitrary field can be written as a product of two matrices with prescribed eigenvalues. Except when is a nonzero nilpotent, the condition is that the number of zeros among the eigenvalues of the factors is not less than the nullity of . 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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DOI:
https://doi.org/10.1090/S0002-9939-1992-1097352-4

Article copyright:
© Copyright 1992
American Mathematical Society