Results 31 to 40 of about 23,326 (218)
VanderLaan Circulant Type Matrices
Abstract and Applied Analysis, 2015 Circulant matrices have become a satisfactory tools in control methods for modern complex systems. In the paper, VanderLaan circulant type matrices are presented, which include VanderLaan circulant, left circulant, and g-circulant matrices.
Hongyan Pan, Zhaolin Jiang
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Alternative proofs of some formulas for two tridiagonal determinants
Acta Universitatis Sapientiae: Mathematica, 2018 In the paper, the authors provide five alternative proofs of two formulas for a tridiagonal determinant, supply a detailed proof of the inverse of the corresponding tridiagonal matrix, and provide a proof for a formula of another tridiagonal determinant.
Qi Feng, Liu Ai-Qi
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On an inverse formula of a tridiagonal matrix [PDF]
Operators and Matrices, 2012 This paper provides an inverse formula freed of determinant expressions for a general tridiagonal matrix. This is viewed as an alternative version of the Usmani formula, which easily tends to blow up computationally. We discuss a number of different viewpoints regarding the proposed and Usmani’s formulas, such as the proof method and the meaning of ...
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Some trace formulae involving the split sequences of a Leonard pair [PDF]
, 2005 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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Orthogonal diagonalization for complex skew-persymmetric anti-tridiagonal Hankel matrices
Special Matrices, 2016 In this paper, we obtain an eigenvalue decomposition for any complex skew-persymmetric anti-tridiagonal Hankel matrix where the eigenvector matrix is orthogonal.
Gutiérrez-Gutiérrez Jesús +1 more
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Inverses of quasi-tridiagonal matrices [PDF]
, 1984 Discretizations in various types of problems lead to quasi-tridiagonal matrices. In this paper, the inverse of a (nonsingular) quasi-tridiagonal matrix is obtained.
Rizvi, S.A.H.
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From superintegrability to tridiagonal representation of β-ensembles
Physics Letters B, 2022 The wonderful formulas by I. Dumitriu and A. Edelman [1,2] rewrite β-ensemble, with eigenvalue integrals containing Vandermonde factors in the power 2β, through integrals over tridiagonal matrices, where β-dependent are the powers of individual matrix ...
A. Mironov, A. Morozov, A. Popolitov
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Bidiagonalization of (k, k + 1)-tridiagonal matrices
Special Matrices, 2019 In this paper,we present the bidiagonalization of n-by-n (k, k+1)-tridiagonal matriceswhen n < 2k. Moreover,we show that the determinant of an n-by-n (k, k+1)-tridiagonal matrix is the product of the diagonal elements and the eigenvalues of the matrix ...
Takahira S., Sogabe T., Usuda T.S.
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Determinants and inverses of perturbed periodic tridiagonal Toeplitz matrices
Advances in Difference Equations, 2019 In this paper, we deal mainly with a class of periodic tridiagonal Toeplitz matrices with perturbed corners. By matrix decomposition with the Sherman–Morrison–Woodbury formula and constructing the corresponding displacement of matrices we derive the ...
Yunlan Wei +3 more
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Inversion of Jacobi's tridiagonal matrix
Computers & Mathematics with Applications, 1994 AbstractThis paper gives a simple algorithm for finding the explicit inverse of a general Jacobi tridiagonal matrix. A few illustrations are also provided to demonstrate the applicability of our algorithm.
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