Two linear transformations each tridiagonal with respect to an eigenbasis of the other: comments on the split decomposition
Two linear transformations each tridiagonal with respect to an eigenbasis of the other: comments on the split decomposition
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两个线性变换，每个变换都相对于另一个的特征基为三对角：对分裂分解的评论
DOI：
10.1016/j.cam.2004.04.017
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发表时间：
2003
影响因子：
2.4
通讯作者：
Paul M. Terwilliger
中科院分区：
文献类型：
--
作者：
Paul M. Terwilliger
设K表示域，V表示K上的有限正维数向量空间。我们考虑一个线性变换A：V→V和A*：V→V的有序对，它们满足以下两个条件：我们称这样的对为V上的伦纳德对。参考上面的伦纳德对，已知存在V到一维子空间的直和的分解，A以下双对角方式作用在该子空间上，A* 以上双对角方式作用在该子空间上。这被称为分裂分解。本文给出了包含分裂分解的伦纳德对的两个刻画。
Let K denote a field and let V denote a vector space over K with finite positive dimension. We consider an ordered pair of linear transformations A:V→V and A*:V→V that satisfy both conditions below:We call such a pair a Leonard pair on V. Referring to the above Leonard pair, it is known there exists a decomposition of V into a direct sum of one-dimensional subspaces, on which A acts in a lower bidiagonal fashion and A*acts in an upper bidiagonal fashion. This is called the split decomposition. In this paper, we give two characterizations of a Leonard pair that involve the split decomposition.