| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4599063 | Linear Algebra and its Applications | 2015 | 52 Pages |
Abstract
Fix an algebraically closed field FF and an integer n≥1n≥1. Let Matn(F)Matn(F) denote the FF-algebra consisting of the n×nn×n matrices that have all entries in FF. We consider a pair of diagonalizable matrices in Matn(F)Matn(F), each acting in an irreducible tridiagonal fashion on an eigenbasis for the other one. Such a pair is called a Leonard pair in Matn(F)Matn(F). In the present paper, we find all Leonard pairs A , A⁎A⁎ in Matn(F)Matn(F) such that each of A and A⁎A⁎ is irreducible tridiagonal with all diagonal entries 0. This solves a problem given by Paul Terwilliger.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Kazumasa Nomura,