On the Relationship Between the Multiplicities of the Matrix Spectrum and the Signs of the Components of its Eigenvectors in a Tree-Like Structure

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On the Relationship Between the Multiplicities of the Matrix Spectrum and the Signs of the Components of its Eigenvectors in a Tree-Like Structure. / Buslov, V. A. .

в: Journal of Mathematical Sciences, Том 236, № 5, 01.02.2019, стр. 477-489.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{572fb3be78db49f2895e079434d7d8c9,

title = "On the Relationship Between the Multiplicities of the Matrix Spectrum and the Signs of the Components of its Eigenvectors in a Tree-Like Structure",

abstract = "We obtain a tree-like parametric representation of the eigenspace corresponding to an eigenvalue ⋋ of a matrix G in the case where the matrix G − ⋋E has a nonzero principal basic minor. If the algebraic and geometric multiplicities of ⋋ coincide, then such a minor always exists. The coefficients of powers of the spectral parameter are sums of terms of the same sign. If there is no nonzero principal basic minor, then the tree-like form does not allow one to represent the coefficients as sums of terms of the same sign, the only exception being the case of an eigenvalue of geometric multiplicity 1.",

author = "Buslov, {V. A.}",

year = "2019",

month = feb,

day = "1",

doi = "10.1007/s10958-018-4126-0",

language = "English",

volume = "236",

pages = "477--489",

journal = "Journal of Mathematical Sciences",

issn = "1072-3374",

publisher = "Springer Nature",

number = "5",

}

RIS

TY - JOUR

T1 - On the Relationship Between the Multiplicities of the Matrix Spectrum and the Signs of the Components of its Eigenvectors in a Tree-Like Structure

AU - Buslov, V. A.

PY - 2019/2/1

Y1 - 2019/2/1

N2 - We obtain a tree-like parametric representation of the eigenspace corresponding to an eigenvalue ⋋ of a matrix G in the case where the matrix G − ⋋E has a nonzero principal basic minor. If the algebraic and geometric multiplicities of ⋋ coincide, then such a minor always exists. The coefficients of powers of the spectral parameter are sums of terms of the same sign. If there is no nonzero principal basic minor, then the tree-like form does not allow one to represent the coefficients as sums of terms of the same sign, the only exception being the case of an eigenvalue of geometric multiplicity 1.

AB - We obtain a tree-like parametric representation of the eigenspace corresponding to an eigenvalue ⋋ of a matrix G in the case where the matrix G − ⋋E has a nonzero principal basic minor. If the algebraic and geometric multiplicities of ⋋ coincide, then such a minor always exists. The coefficients of powers of the spectral parameter are sums of terms of the same sign. If there is no nonzero principal basic minor, then the tree-like form does not allow one to represent the coefficients as sums of terms of the same sign, the only exception being the case of an eigenvalue of geometric multiplicity 1.

UR - http://www.scopus.com/inward/record.url?scp=85058435538&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/relationship-between-multiplicities-matrix-spectrum-signs-components-eigenvectors-treelike-structure

U2 - 10.1007/s10958-018-4126-0

DO - 10.1007/s10958-018-4126-0

M3 - Article

VL - 236

SP - 477

EP - 489

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 5

ER -

ID: 37664023