Results 21 to 30 of about 23,326 (218)
Positive Integer Powers of Certain Tridiagonal Matrices and Corresponding Anti-Tridiagonal Matrices
Advances in Mathematical Physics, 2022 In this paper, we firstly derive a general expression for the entries of the mth (m∈ℕ) power for two certain types of tridiagonal matrices of arbitrary order. Secondly, we present a method for computing the positive integer powers of the anti-tridiagonal
Mohammad Beiranvand +1 more
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The complete positivity of symmetric tridiagonal and pentadiagonal matrices
Special Matrices, 2022 We provide a decomposition that is sufficient in showing when a symmetric tridiagonal matrix AA is completely positive. Our decomposition can be applied to a wide range of matrices.
Cao Lei, McLaren Darian, Plosker Sarah
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Linear transformations that are tridiagonal with respect to both eigenbases of a Leonard pair [PDF]
, 2006 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 $A : V \to V$ and $A^* : V \to V$ that satisfy (i) and (ii) below: (i) There exists a basis for $V$ with ...
Nomura, Kazumasa, Terwilliger, Paul
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Identities and exponential bounds for transfer matrices [PDF]
, 2012 This paper is about analytic properties of single transfer matrices originating from general block-tridiagonal or banded matrices. Such matrices occur in various applications in physics and numerical analysis.
Molinari, Luca G
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The eigenvalues of a tridiagonal matrix in biogeography [PDF]
Applied Mathematics and Computation, 2011 We derive the eigenvalues of a tridiagonal matrix with a special structure. A conjecture about the eigenvalues was presented in a previous paper, and here we prove the conjecture. The matrix structure that we consider has applications in biogeography theory.
Dan Simon, B. Igelnik
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On decomposition of k-tridiagonal ℓ-Toeplitz matrices and its applications
Special Matrices, 2015 We consider a k-tridiagonal ℓ-Toeplitz matrix as one of generalizations of a tridiagonal Toeplitz matrix. In the present paper, we provide a decomposition of the matrix under a certain condition.
Ohashi A., Sogabe T., Usuda T.S.
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The Explicit Inverse of a Tridiagonal Matrix [PDF]
Mathematics of Computation, 1970 The closed form inverse of a tridiagonal matrix, which is a slight generalization of a matrix considered by D. Kershaw (Math. Comp., v. 23, 1969, pp. 189–191), is given in this note. If the matrix has integer elements, an integer multiple of the inverse can be computed by integer arithmetic, that is, without machine roundoff error.
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Matrix units associated with the split basis of a Leonard pair [PDF]
, 2006 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 $A:V \to V$ and $A^*:V \to V$ that satisfy (i), (ii) below: (i) There exists a basis for $V$ with respect to
Nomura, Kazumasa, Terwilliger, Paul
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Remark on the eigenvalues of a tridiagonal matrix in biogeography
Applied Mathematics and Computation, 2023 The main result proved in [The eigenvalues of a tridiagonal matrix in biogeography, Appl. Math. Comput. 218 (2011) 195-201; MR2821464] by B. Igelnik and D. Simon is virtually the Sylvester determinant.
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Determinants of Block Tridiagonal Matrices [PDF]
, 2008 An identity is proven that evaluates the determinant of a block tridiagonal matrix with (or without) corners as the determinant of the associated transfer matrix (or a submatrix of it).Comment: 8 pages, final form.
Molinari, Luca G.
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