Cofactors and eigenvectors of banded Toeplitz matrices: Trench formulas via skew Schur polynomials

Egor A. Maximenko, Mario Alberto Moctezuma-Salazar

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

The Jacobi–Trudi formulas imply that the minors of the banded Toeplitz matrices can be written as certain skew Schur polynomials. In 2012, Alexandersson expressed the corresponding skew partitions in terms of the indices of the struck-out rows and columns. In the present paper, we develop the same idea and obtain some new applications. First, we prove a slight generalization and modification of Alexandersson’s formula. Then, we deduce corollaries about the cofactors and eigenvectors of banded Toeplitz matrices, and give new simple proofs to the corresponding formulas published by Trench in 1985.

Original languageEnglish
Pages (from-to)1149-1169
Number of pages21
JournalOperators and Matrices
Volume11
Issue number4
DOIs
StatePublished - Dec 2017

Keywords

  • Cofactor
  • Eigenvector
  • Minor
  • Skew Schur function
  • Toeplitz matrix

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