2017
DOI: 10.1016/j.laa.2017.01.026
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Bidiagonal triples

Abstract: We introduce a linear algebraic object called a bidiagonal triple. A bidiagonal triple consists of three diagonalizable linear transformations on a finite-dimensional vector space, each of which acts in a bidiagonal fashion on the eigenspaces of the other two. The concept of bidiagonal triple is a generalization of the previously studied and similarly defined concept of bidiagonal pair. We show that every bidiagonal pair extends to a bidiagonal triple, and we describe the sense in which this extension is uniqu… Show more

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Cited by 6 publications
(2 citation statements)
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“…Tridiagonal pairs have been used to investigate the open XXZ spin chain and related models in statistical mechanics (see [16][17][18][19][20][21][22]). The study of tridiagonal pairs has lead to some conceptual advances, such as the bidiagonal pairs/triples (see [43,44]), the billiard arrays (see [148,163]), Hessenberg pairs (see [49][50][51]), and the lowering-raising triples (see [103,104,149]).…”
Section: Casementioning
confidence: 99%
“…Tridiagonal pairs have been used to investigate the open XXZ spin chain and related models in statistical mechanics (see [16][17][18][19][20][21][22]). The study of tridiagonal pairs has lead to some conceptual advances, such as the bidiagonal pairs/triples (see [43,44]), the billiard arrays (see [148,163]), Hessenberg pairs (see [49][50][51]), and the lowering-raising triples (see [103,104,149]).…”
Section: Casementioning
confidence: 99%
“…Tridiagonal pairs have been used to investigate the open XXZ spin chain and related models in statistical mechanics (see [16][17][18][19][20][21][22]). The study of tridiagonal pairs has lead to some conceptual advances, such as the bidiagonal pairs/triples (see [43,44]), the billiard…”
Section: Casementioning
confidence: 99%