S. Kouachi (2008)
Applicationes Mathematicae
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We give explicit expressions for the eigenvalues and eigenvectors of some tridiagonal matrices with non-constant diagonal entries. Our techniques are based on the theory of recurrent sequences.
Adam Czornik, Piotr Jurgas (2006)
International Journal of Applied Mathematics and Computer Science
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In this paper we show new formulas for the spectral radius and the spectral subradius of a set of matrices. The advantage of our results is that we express the spectral radius of any set of matrices by the spectral radius of a set of symmetric positive definite matrices. In particular, in one of our formulas the spectral radius is expressed by singular eigenvalues of matrices, whereas in the existing results it is expressed by eigenvalues.
N. A. Balonin, D. Ž. Ðokovic, D. A. Karbovskiy (2018)
Special Matrices
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We continue our systematic search for symmetric Hadamard matrices based on the so called propus construction. In a previous paper this search covered the orders 4v with odd v ≤ 41. In this paper we cover the cases v = 43, 45, 47, 49, 51. The odd integers v < 120 for which no symmetric Hadamard matrices of order 4v are known are the following: 47, 59, 65, 67, 73, 81, 89, 93, 101, 103, 107, 109, 113, 119. By using the propus construction, we found several symmetric Hadamard matrices...
B.N. Parlett, W.-D. Wu (1984)
Numerische Mathematik
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Meenakshi, Ar., Krishnaswamy, D. (2002)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
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Knudsen, C., McDonald, J.J. (2001)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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Olivia Di Matteo, Dragomir Ž. Ðoković, Ilias S. Kotsireas (2015)
Special Matrices
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We construct new symmetric Hadamard matrices of orders 92, 116, and 172. While the existence of those of order 92 was known since 1978, the orders 116 and 172 are new. Our construction is based on a recent new combinatorial array (GP array) discovered by N. A. Balonin and J. Seberry. For order 116 we used an adaptation of an algorithm for parallel collision search. The adaptation pertains to the modification of some aspects of the algorithm to make it suitable to solve a 3-way matching...
Hershkowitz, Daniel, Keller, Nathan (2005)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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Gil, Michael I. (2002)
Applied Mathematics E-Notes [electronic only]
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Miroslav Fiedler (1974)
Acta Universitatis Carolinae. Mathematica et Physica
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M. Capitaine, C. Donati-Martin, D. Féral (2012)
Annales de l'I.H.P. Probabilités et statistiques
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In this paper, we study the fluctuations of the extreme eigenvalues of a spiked finite rank deformation of a Hermitian (resp. symmetric) Wigner matrix when these eigenvalues separate from the bulk. We exhibit quite general situations that will give rise to universality or non-universality of the fluctuations, according to the delocalization or localization of the eigenvectors of the perturbation. Dealing with the particular case of a spike with multiplicity one, we also establish a necessary...
Ikramov, Kh.D., Nazari, A.M. (2005)
Zapiski Nauchnykh Seminarov POMI
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Gašper Zadnik (2014)
Colloquium Mathematicae
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We classify the isometries in the non-identity component of the whole isometry group of the symmetric space of positive 3 × 3 matrices of determinant 1: we determine the translation lengths, minimal spaces and fixed points at infinity.