Some results on numerical ranges and factorizations of matrix polynomials

Alexander S. Markus; Leiba Rodman

doi:10.1080/03081089708818497

Some results on numerical ranges and factorizations of matrix polynomials

Alexander S. Markus, Leiba Rodman

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

Some new factorization theorems for monic matrix polynomials are obtained. These theorems are based on the numerical range having the number of connected components equal to the degree of the polynomial. For second degree polynomials, sufficient conditions are given for the numerical range to have two connected components.

Original language	English
Pages (from-to)	169-185
Number of pages	17
Journal	Linear and Multilinear Algebra
Volume	42
Issue number	2
DOIs	https://doi.org/10.1080/03081089708818497
State	Published - 1 Jan 1997

Keywords

Factorization
Matrix polynomials
Numerical range
Operator polynomials

ASJC Scopus subject areas

Algebra and Number Theory

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10.1080/03081089708818497

Cite this

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title = "Some results on numerical ranges and factorizations of matrix polynomials",

abstract = "Some new factorization theorems for monic matrix polynomials are obtained. These theorems are based on the numerical range having the number of connected components equal to the degree of the polynomial. For second degree polynomials, sufficient conditions are given for the numerical range to have two connected components.",

keywords = "Factorization, Matrix polynomials, Numerical range, Operator polynomials",

author = "Markus, {Alexander S.} and Leiba Rodman",

note = "Funding Information: he research of this author is partially supported by the NSF Grant DMS-9500924.",

year = "1997",

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doi = "10.1080/03081089708818497",

language = "English",

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AU - Markus, Alexander S.

AU - Rodman, Leiba

N1 - Funding Information: he research of this author is partially supported by the NSF Grant DMS-9500924.

PY - 1997/1/1

Y1 - 1997/1/1

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AB - Some new factorization theorems for monic matrix polynomials are obtained. These theorems are based on the numerical range having the number of connected components equal to the degree of the polynomial. For second degree polynomials, sufficient conditions are given for the numerical range to have two connected components.

KW - Factorization

KW - Matrix polynomials

KW - Numerical range

KW - Operator polynomials

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DO - 10.1080/03081089708818497

M3 - Article

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EP - 185

JO - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

IS - 2

ER -

Some results on numerical ranges and factorizations of matrix polynomials

Abstract

Keywords

ASJC Scopus subject areas

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