Displaying similar documents to “Multiplicative Cauchy functional equation in the cone of positive-definite symmetric matrices”

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...

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.

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...

An analytic characterization of the symmetric extension of a Herglotz-Nevanlinna function

Mitja Nedic (2023)

Czechoslovak Mathematical Journal

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We derive an analytic characterization of the symmetric extension of a Herglotz-Nevanlinna function. Here, the main tools used are the so-called variable non-dependence property and the symmetry formula satisfied by Herglotz-Nevanlinna and Cauchy-type functions. We also provide an extension of the Stieltjes inversion formula for Cauchy-type and quasi-Cauchy-type functions.

The Lukacs-Olkin-Rubin theorem on symmetric cones through Gleason's theorem

Bartosz Kołodziejek (2013)

Studia Mathematica

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We prove the Lukacs characterization of the Wishart distribution on non-octonion symmetric cones of rank greater than 2. We weaken the smoothness assumptions in the version of the Lukacs theorem of [Bobecka-Wesołowski, Studia Math. 152 (2002), 147-160]. The main tool is a new solution of the Olkin-Baker functional equation on symmetric cones, under the assumption of continuity of respective functions. It was possible thanks to the use of Gleason's theorem.

E-symmetric numbers

Gang Yu (2005)

Colloquium Mathematicae

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A positive integer n is called E-symmetric if there exists a positive integer m such that |m-n| = (ϕ(m),ϕ(n)), and n is called E-asymmetric if it is not E-symmetric. We show that there are infinitely many E-symmetric and E-asymmetric primes.

On Majorization for Matrices

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...