منابع مشابه
Towards a classification of the tridiagonal pairs
Let K denote a field and let V denote a vector space over K with finite positive dimension. Let End(V ) denote the K-algebra consisting of all K-linear transformations from V to V . We consider a pair A,A ∈ End(V ) that satisfy (i)–(iv) below: (i) Each of A,A is diagonalizable. (ii) There exists an ordering {Vi} d i=0 of the eigenspaces of A such that A Vi ⊆ Vi−1+ Vi + Vi+1 for 0 ≤ i ≤ d, where...
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We consider the reduction of a symmetric indefinite matrix pair (A,B), with B nonsingular, to tridiagonal-diagonal form by congruence transformations. This is an important reduction in solving polynomial eigenvalue problems with symmetric coefficient matrices and in frequency response computations. The pair is first reduced to symmetric-diagonal form. We describe three methods for reducing the ...
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Let F denote an algebraically closed field with characteristic 0 and let V denote a vector space over F 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 {d − 2i}i=0 is a standard ordering of the eigenvalues of A and a standard ordering of the eigenvalues of A. Assume A,A has Krawtchouk type. We show...
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Let K denote a field and let V denote a vector space over K with finite positive dimension. We consider a pair of linear transformations A : V → V and A∗ : V → V that satisfy the following conditions: (i) each of A,A∗ is diagonalizable; (ii) there exists an ordering {Vi} d i=0 of the eigenspaces of A such that A ∗Vi ⊆ Vi−1+Vi+Vi+1 for 0 ≤ i ≤ d, where V−1 = 0 and Vd+1 = 0; (iii) there exists an...
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Let K denote an algebraically closed field and let q denote a nonzero scalar in K that is not a root of unity. Let V denote a vector space over K with finite positive dimension and let A,A denote a tridiagonal pair on V . Let θ0, θ1, . . . , θd (resp. θ ∗ 0, θ ∗ 1, . . . , θ ∗ d) denote a standard ordering of the eigenvalues of A (resp. A). We assume there exist nonzero scalars a, a in K such t...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2008
ISSN: 0024-3795
DOI: 10.1016/j.laa.2008.02.006