Strong shift equivalence and the Generalized Spectral Conjecture for nonnegative matrices

Mike Boyle*, Scott Schmieding

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Given matrices A and B shift equivalent over a dense subring R of ℝ, with A primitive, we show that B is strong shift equivalent over R to a primitive matrix. This result shows that the weak form of the Generalized Spectral Conjecture for primitive matrices implies the strong form. The foundation of this work is the recent result that for any ring R, the group NK1(R) of algebraic K-theory classifies the refinement of shift equivalence by strong shift equivalence for matrices over R.

Original languageEnglish (US)
Pages (from-to)231-243
Number of pages13
JournalLinear Algebra and Its Applications
Volume498
DOIs
StatePublished - Jun 1 2016

Keywords

  • Nonnegative matrix
  • Shift equivalence
  • Spectra
  • Spectral conjecture

ASJC Scopus subject areas

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

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