Bounds for the spectrum of a two parameter matrix eigenvalue problem

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Abstract

We consider the two parameter eigenvalue problem Tjvj - λ1Aj1vj - λ2Aj2vj = 0, where λj C; Tj, Ajk (j,k=1,2) are matrices. Bounds for the spectral radius of that problem are suggested. Our main tool is a norm estimate for the operator inverse to the operator A11 ⊗ A22 - A12 ⊗ A21, where ⊗ means the tensor product. In addition, by virtue of that norm estimate and the Ostrowsky-Schneider theorem we establish a condition that provides the conservation of the number of the eigenvalues of the considered problem in a half-plane.

Original languageEnglish
Pages (from-to)201-218
Number of pages18
JournalLinear Algebra and Its Applications
Volume498
DOIs
StatePublished - 1 Jun 2016

Keywords

  • Ostrowsky-Schneider theorem
  • Spectrum
  • Two parameter matrix eigenvalue problem

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