Factorization of Selfadjoint Quadratic Matrix Polynomials with Real Spectrum

Ilya Krupnik; Alexander Markus; Peter Lancaster

doi:10.1080/03081089508818400

Factorization of Selfadjoint Quadratic Matrix Polynomials with Real Spectrum

Ilya Krupnik, Alexander Markus, Peter Lancaster

Department of Mathematics

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

5 Scopus citations

Abstract

Factorization theorems, and properties of sets of eigenvectors, are established for regular selfadjoint quadratic matrix polynomials L(λ) whose leading coefficient is indefinite or possibly singular, and for which all eigenvalues are real of definite type. The two linear factors obtained have spectra which are just the eigenvalues of L(λ) of positive and negative types, respectively.

Original language	English
Pages (from-to)	263-272
Number of pages	10
Journal	Linear and Multilinear Algebra
Volume	39
Issue number	3
DOIs	https://doi.org/10.1080/03081089508818400
State	Published - 1 Aug 1995

ASJC Scopus subject areas

Algebra and Number Theory

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10.1080/03081089508818400

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title = "Factorization of Selfadjoint Quadratic Matrix Polynomials with Real Spectrum",

abstract = "Factorization theorems, and properties of sets of eigenvectors, are established for regular selfadjoint quadratic matrix polynomials L(λ) whose leading coefficient is indefinite or possibly singular, and for which all eigenvalues are real of definite type. The two linear factors obtained have spectra which are just the eigenvalues of L(λ) of positive and negative types, respectively.",

author = "Ilya Krupnik and Alexander Markus and Peter Lancaster",

year = "1995",

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doi = "10.1080/03081089508818400",

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journal = "Linear and Multilinear Algebra",

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T1 - Factorization of Selfadjoint Quadratic Matrix Polynomials with Real Spectrum

AU - Krupnik, Ilya

AU - Markus, Alexander

AU - Lancaster, Peter

PY - 1995/8/1

Y1 - 1995/8/1

N2 - Factorization theorems, and properties of sets of eigenvectors, are established for regular selfadjoint quadratic matrix polynomials L(λ) whose leading coefficient is indefinite or possibly singular, and for which all eigenvalues are real of definite type. The two linear factors obtained have spectra which are just the eigenvalues of L(λ) of positive and negative types, respectively.

AB - Factorization theorems, and properties of sets of eigenvectors, are established for regular selfadjoint quadratic matrix polynomials L(λ) whose leading coefficient is indefinite or possibly singular, and for which all eigenvalues are real of definite type. The two linear factors obtained have spectra which are just the eigenvalues of L(λ) of positive and negative types, respectively.

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U2 - 10.1080/03081089508818400

DO - 10.1080/03081089508818400

M3 - Article

AN - SCOPUS:0041904514

SN - 0308-1087

VL - 39

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EP - 272

JO - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

IS - 3

ER -

Factorization of Selfadjoint Quadratic Matrix Polynomials with Real Spectrum

Abstract

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