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| Weyl and Lidski? Inequalities for General Hyperbolic Polynomials |
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Citation： |
Denis SERRE.Weyl and Lidski? Inequalities for General Hyperbolic Polynomials[J].Chinese Annals of Mathematics B,2009,30(6):785~802 |
| Page view： 1719
Net amount： 1101 |
Authors： |
Denis SERRE; |
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| Abstract： |
The roots of hyperbolic polynomials satisfy the linear inequalities that were
previously established for the eigenvalues of Hermitian matrices, after a conjecture by
A. Horn. Among them are the so-called Weyl and Lidski?? inequalities. An elementary
proof of the latter for hyperbolic polynomials is given. This proof follows an idea from
H. Weinberger and is free from representation theory and Schubert calculus arguments, as
well as from hyperbolic partial differential equations theory. |
Keywords： |
Hyperbolic polynomials, Real roots, Eigenvalues of Hermitian matrices |
Classification： |
11C08, 12D10, 26C10 |
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