Results 11 to 20 of about 9,075 (140)
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
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A family of tridiagonal pairs and related symmetric functions [PDF]
Journal of Physics A: Mathematical and General, 2006 A family of tridiagonal pairs which appear in the context of quantum integrable systems is studied in details. The corresponding eigenvalue sequences, eigenspaces and the block tridiagonal structure of their matrix realizations with respect the dual ...
Askey R +11 more
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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
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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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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 $
Ito, Tatsuro, Terwilliger, Paul
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The shape of a tridiagonal pair
Journal of Pure and Applied Algebra, 2004 17 ...
Ito, Tatsuro, 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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Tridiagonal pairs of Krawtchouk type
Linear Algebra and its Applications, 2007 Let $K$ denote an algebraically closed field with characteristic 0 and let $V$ denote a vector space over $K$ with finite positive dimension. Let $A,A^*$ denote a tridiagonal pair on $V$ with diameter $d$. We say that $A,A^*$ has Krawtchouk type whenever the sequence $\lbrace d-2i\rbrace_{i=0}^d$ is a standard ordering of the eigenvalues of $A$ and a ...
Ito, Tatsuro, Terwilliger, Paul
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Tridiagonal-Diagonal Reduction of Symmetric Indefinite Pairs [PDF]
SIAM Journal on Matrix Analysis and Applications, 2004 The authors consider the reduction of a symmetric indefinite matrix pair \((A, B)\), with \(B\) nonsingular, to tridiagonal-diagonal form by congruence transformations. More precisely, three different tridiagonal-diagonal reduction methods are presented. The first two algorithms proposed are an improvement over \textit{M. A.
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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}
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