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Proceedings of the American Mathematical Society

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

 

 

Interlacing polynomials


Author: Charles R. Johnson
Journal: Proc. Amer. Math. Soc. 100 (1987), 401-404
MSC: Primary 15A60; Secondary 12D10
DOI: https://doi.org/10.1090/S0002-9939-1987-0891133-8
MathSciNet review: 891133
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Abstract: Let $ A$ be an $ n$-by-$ n$ Hermitian matrix. We note that the set of all monic, degree $ n - 1$ polynomials whose roots interlace the eigenvalues of $ A$ is exactly the classical field of values of $ \operatorname{adj}(\lambda I - A)$.


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DOI: https://doi.org/10.1090/S0002-9939-1987-0891133-8
Article copyright: © Copyright 1987 American Mathematical Society