Interlacing polynomials
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- by Charles R. Johnson PDF
- Proc. Amer. Math. Soc. 100 (1987), 401-404 Request permission
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 $\operatorname {adj}(\lambda I - A)$.References
- Roger A. Horn and Charles R. Johnson, Matrix analysis, Cambridge University Press, Cambridge, 1985. MR 832183, DOI 10.1017/CBO9780511810817 —, Topics in matrix analysis, Cambridge Univ. Press, New York, 1987. K. Regan, private communication.
Additional Information
- © Copyright 1987 American Mathematical Society
- 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