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A characterization of Leonard pairs using the notion of a tail

Author:
Hanson, Edward  


Journal:
LINEAR ALGEBRA AND ITS APPLICATIONS


Issue Date:
2011


Abstract(summary):

Let V denote a vector space with finite positive dimension. We consider an ordered pair of linear transformations A : V -> V and A* : V -> V that satisfy (i) and (ii) below: (i) There exists a basis for V with respect to which the matrix representing A is irreducible tridiagonal and the matrix representing A* is diagonal. (ii) There exists a basis for V with respect to which the matrix representing A* is irreducible tridiagonal and the matrix representing A is diagonal. We call such a pair a Leonard pair on V. In this paper, we characterize the Leonard pairs using the notion of a tail. This notion is borrowed from algebraic graph theory. (C) 2011 Elsevier Inc. All rights reserved.


Page:
2961---2970


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