Results 11 to 20 of about 9,096 (136)
Tridiagonal pairs of q-Racah type
Journal of Algebra, 2009 Let $K$ denote an algebraically closed field and let $V$ denote a vector space over $K$ with finite positive dimension. We consider a pair of linear transformations $A:V \to V$ and $A^*:V \to V$ that satisfy the following conditions: (i) each of $A,A^*$ is diagonalizable; (ii) there exists an ordering $\lbrace V_i\rbrace_{i=0}^d$ of the eigenspaces of $
Paul M Terwilliger
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The shape of a tridiagonal pair
Journal of Pure and Applied Algebra, 2004 17 ...
Paul M Terwilliger
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Tridiagonal pairs of height one
Linear Algebra and Its Applications, 2005 Let \(V\) be a vector space over field \(F\) with finite positive dimension. Let \((A,A^*)\) be a tridiagonal pair on \(V\), and let \((\rho_0,\dots,\rho_d)\) be the shape of \((A,A^*)\). It is known that there exists a unique integer \(h\) (the height of the tridiagonal pair) with \(0\leq h\leq d/2\) such that \(\rho_{i-1}
Kazumasa Nomura
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Tridiagonal pairs and the Askey–Wilson relations
Linear Algebra and Its Applications, 2005 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kazumasa Nomura
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Tridiagonal pairs, alternating elements, and distance-regular graphs
Journal of Combinatorial Theory - Series A, 2023 39 pages, 9 ...
Paul M Terwilliger
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Linear Algebra and its Applications, 2008 Let $K$ denote a field and let $V$ denote a vector space over $K$ with finite positive dimension. We consider a pair of $K$-linear transformations $A:V \to V$ and $A^*:V \to V$ that satisfies the following conditions: (i) each of $A,A^*$ is diagonalizable; (ii) there exists an ordering ${V_i}_{i=0}^d$ of the eigenspaces of $A$ such that $A^* V_i ...
Nomura, Kazumasa, Terwilliger, Paul
+12 more sources
Tridiagonal pairs of shape (1,2,1)
Linear Algebra and its Applications, 2008 Let $\mathbb F$ denote a field and let $V$ denote a vector space over $\mathbb F$ with finite positive dimension. We consider a pair of linear transformations $A:V\to V$ and $A^*:V\to V$ that satisfies the following conditions: (i) each of $A,A^*$ is diagonalizable; (ii) there exists an ordering $\lbrace V_i \rbrace_{i=0}^d$ of the eigenspaces of $A ...
Ito, Tatsuro +2 more
+18 more sources
Linear transformations that are tridiagonal with respect to both eigenbases of a Leonard pair
Linear Algebra and Its Applications, 2007 12 ...
Kazumasa Nomura, Paul M Terwilliger
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Totally bipartite tridiagonal pairs
The Electronic Journal of Linear Algebra, 2021 There is a concept in linear algebra called a tridiagonal pair. The concept was motivated by the theory of $Q$-polynomial distance-regular graphs. We give a tutorial introduction to tridiagonal pairs, working with a special case as a concrete example. The special case is called totally bipartite, or totally bipartite (TB).
Nomura, Kazumasa, Terwilliger, Paul
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Linear Algebra and its Applications, 2004 Let \(V\) be a vector space of finite dimension over a field, and let \(A, A^*\) be a tridiagonal pair on \(V\) of diameter at least 3, whose eigenvalue and dual eigenvalue sequences, not all having multiplicity one, satisfy certain conditions. Given \(V = Mv^* + M^*v\), where \(M\) and \(M^*\) are the subalgebras of End\((V)\) generated by \(A, A^*\),
Alnajjar, Hasan, Curtin, Brian
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