A surjectivity problem for 3 by 3 matrices

Constantin Buşe; Donal O’regan; Olivia Saierli

doi:10.7153/oam-2019-13-07

A surjectivity problem for 3 by 3 matrices

Constantin Buşe, Donal O’regan, Olivia Saierli

Mathematics

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

4 Citations (Scopus)

Abstract

Let P be a complex polynomial. We prove that the associated polynomial matrix-valued function \P is surjective if and only if for each λ ∈ C the polynomial P − λ has at least a simple zero.

Original language	English
Article number	13-07
Pages (from-to)	111-119
Number of pages	9
Journal	Operators and Matrices
Volume	13
Issue number	1
DOIs	https://doi.org/10.7153/oam-2019-13-07
Publication status	Published - Mar 2019

Keywords

Functional calculus with matrices
Global problems concerning polynomials of matrices
Natural powers of matrices

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title = "A surjectivity problem for 3 by 3 matrices",

abstract = "Let P be a complex polynomial. We prove that the associated polynomial matrix-valued function \textbackslash{}P is surjective if and only if for each λ ∈ C the polynomial P − λ has at least a simple zero.",

keywords = "Functional calculus with matrices, Global problems concerning polynomials of matrices, Natural powers of matrices",

author = "Constantin Bu{\c s}e and Donal O{\textquoteright}regan and Olivia Saierli",

year = "2019",

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doi = "10.7153/oam-2019-13-07",

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AU - Saierli, Olivia

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AB - Let P be a complex polynomial. We prove that the associated polynomial matrix-valued function \P is surjective if and only if for each λ ∈ C the polynomial P − λ has at least a simple zero.

KW - Functional calculus with matrices

KW - Global problems concerning polynomials of matrices

KW - Natural powers of matrices

UR - https://www.scopus.com/pages/publications/85065489213

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DO - 10.7153/oam-2019-13-07

M3 - Article

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JF - Operators and Matrices

IS - 1

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A surjectivity problem for 3 by 3 matrices

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