Identities for sums of characteristic values of entire matrix pencils

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1 Scopus citations


The paper deals with an entire matrix-valued function of a complex argument (an entire matrix pencil) f of order ρ (f) < ∞. Identities for the following sums of the characteristic values zk (f) (k = 1, 2, ...) of f are established:underover(∑, k = 1, ∞) frac(1, zkm (f)) (m > ρ (f))andunderover(∑, k = 1, ∞) fenced(Im frac(1, zk (f)))2 (ρ (f) < 2) .The suggested results are new even for polynomial pencils.

Original languageEnglish
Pages (from-to)814-823
Number of pages10
JournalLinear Algebra and Its Applications
Issue number4
StatePublished - 1 Feb 2008


  • Characteristic values
  • Entire matrix pencils

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


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