Relationship between the zeros of two polynomials

DOI10.1016/j.laa.2009.07.028zbMath1182.30007OpenAlexW2088774454MaRDI QIDQ1044589

J. Blot

Publication date: 18 December 2009

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2009.07.028

zbMATH Keywords

zeros of polynomialsSchoenberg conjectureWeinstein-Aronszajn formula\(D\)-companion matrixSendov conjecture

Mathematics Subject Classification ID

Inequalities involving eigenvalues and eigenvectors (15A42) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Polynomials and rational functions of one complex variable (30C10)

Related Items (10)

Circulants and critical points of polynomials ⋮ On the realizability of the critical points of a realizable List ⋮ Unnamed Item ⋮ Integrability of matrices ⋮ Skew-circulant matrix and critical points of polynomials ⋮ On the local pairing behavior of critical points and roots of random polynomials ⋮ Pairing between zeros and critical points of random polynomials with independent roots ⋮ Integrability of diagonalizable matrices and a dual Schoenberg type inequality ⋮ Remarks on circulant matrices and critical points of polynomials ⋮ Higher-order, polar and Sz.-Nagy's generalized derivatives of random polynomials with independent and identically distributed zeros on the unit circle

Cites Work

• Differentiators and the geometry of polynomials.
• An analog of the Poincaré separation theorem for normal matrices and the Gauss-Lucas theorem
• A companion matrix approach to the study of zeros and critical points of a polynomial
• Differential-Difference Operators Associated to Reflection Groups
• Bending Flows for Sums of Rank One Matrices
• Inverse spectral problem for normal matrices and the Gauss-Lucas theorem
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