Displaying similar documents to “Weakly sign-symmetric matrices and some determinantal inequalities”

On nowhere weakly symmetric functions and functions with two-element range

Krzysztof Ciesielski, Kandasamy Muthuvel, Andrzej Nowik (2001)

Fundamenta Mathematicae

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A function f: ℝ → {0,1} is weakly symmetric (resp. weakly symmetrically continuous) at x ∈ ℝ provided there is a sequence hₙ → 0 such that f(x+hₙ) = f(x-hₙ) = f(x) (resp. f(x+hₙ) = f(x-hₙ)) for every n. We characterize the sets S(f) of all points at which f fails to be weakly symmetrically continuous and show that f must be weakly symmetric at some x ∈ ℝ∖S(f). In particular, there is no f: ℝ → {0,1} which is nowhere weakly symmetric. It is also shown that if at each...

Construction of symmetric Hadamard matrices of order 4v for v = 47, 73, 113

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...

Symmetric Hadamard matrices of order 116 and 172 exist

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...

On isometries of the symmetric space P₁(3,ℝ)

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.