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- Author:
- Hanson, Edward
- Journal:
- LINEAR ALGEBRA AND ITS APPLICATIONS
- Issue Date:
- 2013
- 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. Arlene Pascasio recently obtained a characterization of the Q-polynomial distance-regular graphs using the intersection numbers a(i). In this paper, we extend her results to a linear algebraic level and obtain a characterization of Leonard pairs. Pascasio's argument appears to rely on the underlying combinatorial assumptions, so we take a different approach that is algebraic in nature. (C) 2012 Published by Elsevier Inc.
- Page:
- 2289---2305

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