Gauss sums and the matrix equation over fields of characteristic two
John Perkins (1971)
Acta Arithmetica
Philip Buckhiester (1973)
Acta Arithmetica
Su, Zhonggen (2006)
Electronic Journal of Probability [electronic only]
Jonas Gustavsson (2005)
Annales de l'I.H.P. Probabilités et statistiques
Shaofang Hong (2002)
Acta Arithmetica
Keiner, Jens (2008)
ETNA. Electronic Transactions on Numerical Analysis [electronic only]
Dolinar, Gregor, Kuzma, Bojan (2008)
ELA. The Electronic Journal of Linear Algebra [electronic only]
Lascoux, Alain (2009)
Séminaire Lotharingien de Combinatoire [electronic only]
Ljiljana Cvetković, Vladimir Kostić, Maja Nedović (2015)
Open Mathematics
In this paper we present a nonsingularity result which is a generalization of Nekrasov property by using two different permutations of the index set. The main motivation comes from the following observation: matrices that are Nekrasov matrices up to the same permutations of rows and columns, are nonsingular. But, testing all the permutations of the index set for the given matrix is too expensive. So, in some cases, our new nonsingularity criterion allows us to use the results already calculated...
Barry, Paul (2010)
Journal of Integer Sequences [electronic only]
Demeyer, Frank, Kakakhail, Hainya (1991)
International Journal of Mathematics and Mathematical Sciences
Bo Zhou (2002)
Czechoslovak Mathematical Journal
We obtain upper bounds for generalized indices of matrices in the class of nearly reducible Boolean matrices and in the class of critically reducible Boolean matrices, and prove that these bounds are the best possible.
Bayat, Morteza (2011)
ELA. The Electronic Journal of Linear Algebra [electronic only]
Moghaddamfar, Ali Reza, Pooya, S.M.H. (2009)
ELA. The Electronic Journal of Linear Algebra [electronic only]
Liu, Jianzhou, Huang, Rong (2010)
ELA. The Electronic Journal of Linear Algebra [electronic only]
Peart, Paul, Woan, Wen-Jin (2000)
Journal of Integer Sequences [electronic only]
Kim, In-Jae, Olesky, Dale D., Shader, Bryan L., Van Den Driessche, Pauline, Van Der Holst, Hein, Vander Meulen, Kevin N. (2009)
ELA. The Electronic Journal of Linear Algebra [electronic only]
Budden, Mark, Hadavas, Paul, Hoffman, Lorrie, Pretz, Chris (2007)
Applied Mathematics E-Notes [electronic only]
Ziqi Lin, Sijie Liu, Kai-Tai Fang, Yuhui Deng (2016)
Special Matrices
This paper presents an enumeration algorithm to generate all magic squares of order 5 based on the ideas of basic form (Schroeppel [7]) and generating vector which is extension of Frénicle Quads (Ollerenshaw and Bondi [6]). The results lead us to extend Frénicle-Amela patterns from the case of order 4 to the case of order 5, which we refer to Frénicle-Amela-Like patterns. We show that these interesting Frénicle-Amela-Like patterns appear simultaneously. The number of these patterns is also calculated....
Trung Hoa Dinh, Sima Ahsani, Tin-Yau Tam (2016)
Czechoslovak Mathematical Journal
We study some geometric properties associated with the -geometric means of two positive definite matrices and . Some geodesical convexity results with respect to the Riemannian structure of the positive definite matrices are obtained. Several norm inequalities with geometric mean are obtained. In particular, we generalize a recent result of Audenaert (2015). Numerical counterexamples are given for some inequality questions. A conjecture on the geometric mean inequality regarding pairs...