Class numbers of pairs of symmetric matrices
Jin Nakagawa (2002)
Acta Arithmetica
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Jin Nakagawa (2002)
Acta Arithmetica
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Zhang, Xian, Yang, Zhongpeng, Cao, Chongguang (2002)
Applied Mathematics E-Notes [electronic only]
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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...
Thomas A. Brown, Joel H. Spencer (1971)
Colloquium Mathematicae
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Khan, M. Adil, Latif, Naveed, Pecaric, J., Peric, I. (2013)
Mathematica Balkanica New Series
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In this paper, we give several results for majorized matrices by using continuous convex function and Green function. We obtain mean value theorems for majorized matrices and also give corresponding Cauchy means, as well as prove that these means are monotonic. We prove positive semi-definiteness of matrices generated by differences deduced from majorized matrices which implies exponential convexity and log-convexity of these differences and also obtain Lypunov's and Dresher's type inequalities...
Meenakshi, A.R., Krishnamoorthy, S. (1999)
Bulletin of the Malaysian Mathematical Society. Second Series
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Paulus Gerdes (2002)
Visual Mathematics
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Đ. Kurepa (1952)
Matematički Vesnik
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Meenakshi, Ar., Krishnaswamy, D. (2002)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
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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...
Paulus Gerdes (2002)
Visual Mathematics
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Brydon Eastman, Kevin N. Vander Meulen (2016)
Special Matrices
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The class of sparse companion matrices was recently characterized in terms of unit Hessenberg matrices. We determine which sparse companion matrices have the lowest bandwidth, that is, we characterize which sparse companion matrices are permutationally similar to a pentadiagonal matrix and describe how to find the permutation involved. In the process, we determine which of the Fiedler companion matrices are permutationally similar to a pentadiagonal matrix. We also describe how to find...