Results 11 to 20 of about 817,308 (268)
LEONARD PAIRS AND THE ASKEY–WILSON RELATIONS [PDF]
Journal of Algebra and Its Applications, 2004 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 which satisfy the following two properties:(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.
Terwilliger, Paul, Vidunas, Raimundas
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Compatibility and companions for Leonard pairs
The Electronic Journal of Linear Algebra, 2022 In this paper, we introduce the concepts of compatibility and companion for Leonard pairs. These concepts are roughly described as follows. Let $\mathbb{F}$ denote a field, and let $V$ denote a vector space over $\mathbb{F}$ with finite positive dimension.A Leonard pair on $V$ is an ordered pair of diagonalizable $\mathbb{F}$-linear maps $A : V \to V ...
Kazumasa Nomura, Paul Terwilliger
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Linear Algebra and its Applications, 2007 20 ...
Nomura, Kazumasa, Terwilliger, Paul
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Affine transformations of a Leonard pair [PDF]
The Electronic Journal of Linear Algebra, 2007 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 $A : V \to V$ and $A^* : V \to V$ 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 ...
Nomura, Kazumasa, Terwilliger, Paul
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The determinant of AA∗–A∗A for a Leonard pair A, A∗
Linear Algebra and its Applications, 2006 11 ...
Nomura, Kazumasa, Terwilliger, Paul
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Journal of Computational and Applied Mathematics, 2003 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The switching element for a Leonard pair
Linear Algebra and its Applications, 2008 Let $V$ denote a vector space with finite positive dimension. We consider a pair of linear transformations $A : V \to V$ and $A^* : V \to V$ 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.
Nomura, Kazumasa, Terwilliger, Paul
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How to recognize a Leonard pair [PDF]
Linear and Multilinear Algebra, 2019 17 ...
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Askey–Wilson relations and Leonard pairs
Discrete Mathematics, 2008 22 pages; corrected version; the example of Section 2 has the normalization consistent with the rest of the ...
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Totally bipartite/abipartite Leonard pairs and Leonard triples of Bannai/ito type [PDF]
The Electronic Journal of Linear Algebra, 2013 This paper is about three classes of objects: Leonard pairs, Leonard triples, and the finite-dimensional irreducible modules for an algebra $\mathcal{A}$. Let $\K$ denote an algebraically closed field of characteristic zero. Let $V$ denote a vector space over $\K$ with finite positive dimension.
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