A variational principle for eigenvalues of pencils of Hermitian matrices

Paul Binding; Branko Najman; Qiang Ye

doi:10.1007/BF01228041

A variational principle for eigenvalues of pencils of Hermitian matrices

Paul Binding, Branko Najman, Qiang Ye

Producción científica: Article › revisión exhaustiva

13 Citas (Scopus)

Resumen

Let H = (A, B) be a pair of Hermitian N × N matrices. A complex number λ is an eigenvalue of H if det(A - λB) = 0 (we include λ = ∞ if detB = 0). For nonsingular H (i.e., for which some λ is not an eigenvalue), we show precisely which eigenvalues can be characterized as σ⁺_k = sup{inf{x* Ax : x* Bx = 1, x ∈ S}, S ∈ S_k}, S_k being the set of subspaces of C^N of codimension k - 1.

Idioma original	English
Páginas (desde-hasta)	398-422
Número de páginas	25
Publicación	Integral Equations and Operator Theory
Volumen	35
N.º	4
DOI	https://doi.org/10.1007/BF01228041
Estado	Published - nov 1999

Nota bibliográfica

Funding Information:
the Ministry of Science of Croatia *Research supported by NSERC of Canada

Funding Information:
*Research supported by NSERC of Canada and the l.W.Killam Foundation tProfessor Najman died suddenly while this work was at its final stage. His research was supported by

Financiación

the Ministry of Science of Croatia *Research supported by NSERC of Canada *Research supported by NSERC of Canada and the l.W.Killam Foundation tProfessor Najman died suddenly while this work was at its final stage. His research was supported by

Financiadores	Número del financiador
NSERC of Canada
Natural Sciences and Engineering Research Council of Canada
Ministry of Science and Technology, Croatia

ASJC Scopus subject areas

Analysis
Algebra and Number Theory

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10.1007/BF01228041

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title = "A variational principle for eigenvalues of pencils of Hermitian matrices",

abstract = "Let H = (A, B) be a pair of Hermitian N × N matrices. A complex number λ is an eigenvalue of H if det(A - λB) = 0 (we include λ = ∞ if detB = 0). For nonsingular H (i.e., for which some λ is not an eigenvalue), we show precisely which eigenvalues can be characterized as σ+k = sup\{inf\{x* Ax : x* Bx = 1, x ∈ S\}, S ∈ Sk\}, Sk being the set of subspaces of CN of codimension k - 1.",

author = "Paul Binding and Branko Najman and Qiang Ye",

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AU - Najman, Branko

AU - Ye, Qiang

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N2 - Let H = (A, B) be a pair of Hermitian N × N matrices. A complex number λ is an eigenvalue of H if det(A - λB) = 0 (we include λ = ∞ if detB = 0). For nonsingular H (i.e., for which some λ is not an eigenvalue), we show precisely which eigenvalues can be characterized as σ+k = sup{inf{x* Ax : x* Bx = 1, x ∈ S}, S ∈ Sk}, Sk being the set of subspaces of CN of codimension k - 1.

AB - Let H = (A, B) be a pair of Hermitian N × N matrices. A complex number λ is an eigenvalue of H if det(A - λB) = 0 (we include λ = ∞ if detB = 0). For nonsingular H (i.e., for which some λ is not an eigenvalue), we show precisely which eigenvalues can be characterized as σ+k = sup{inf{x* Ax : x* Bx = 1, x ∈ S}, S ∈ Sk}, Sk being the set of subspaces of CN of codimension k - 1.

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A variational principle for eigenvalues of pencils of Hermitian matrices

Resumen

Nota bibliográfica

Financiación

ASJC Scopus subject areas

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