The multiplicative inverse eigenvalue problem over an algebraically closed field

Joachim Rosenthal, Xiaochang Wang

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

Let M be an n × n square matrix and let p(λ) be a monic polynomial of degree n. Let Crossed Z sign be a set of n × n matrices. The multiplicative inverse eigenvalue problem asks for the construction of a matrix Z ∈ Crossed Z sign such that the product matrix MZ has characteristic polynomial p(λ). In this paper we provide new necessary and sufficient conditions when Crossed Z sign is an affine variety over an algebraically closed field.

Original languageEnglish
Pages (from-to)517-523
Number of pages7
JournalSIAM Journal on Matrix Analysis and Applications
Volume23
Issue number2
DOIs
StatePublished - 2002

Keywords

  • Dominant morphism theorem
  • Eigenvalue completion
  • Inverse eigenvalue problems

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