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Displaying 601 – 620 of 941

On the reduction of a random basis

Ali Akhavi, Jean-François Marckert, Alain Rouault (2009)

ESAIM: Probability and Statistics

For p ≤ n, let b1(n),...,bp(n) be independent random vectors in $ℝ^{n}$ with the same distribution invariant by rotation and without mass at the origin. Almost surely these vectors form a basis for the Euclidean lattice they generate. The topic of this paper is the property of reduction of this random basis in the sense of Lenstra-Lenstra-Lovász (LLL). If ${\hat{b}}_{1}^{(n)}, ..., {\hat{b}}_{p}^{(n)}$ is the basis obtained from b1(n),...,bp(n) by Gram-Schmidt orthogonalization, the quality of the reduction depends upon the sequence of ratios...

On the Relationships between Zero Forcing Numbers and Certain Graph Coverings

Fatemeh Alinaghipour Taklimi, Shaun Fallat, Karen Meagher (2014)

Special Matrices

The zero forcing number and the positive zero forcing number of a graph are two graph parameters that arise from two types of graph colourings. The zero forcing number is an upper bound on the minimum number of induced paths in the graph that cover all the vertices of the graph, while the positive zero forcing number is an upper bound on the minimum number of induced trees in the graph needed to cover all the vertices in the graph. We show that for a block-cycle graph the zero forcing number equals...

On the R-Order of Coupled Sequences Arising in Single-Step Type Methods.

J.W. Schmidt, W. Burmeister (1988)

Numerische Mathematik

On the second-order correlation function of the characteristic polynomial of a real symmetric Wigner matrix.

Kösters, Holger (2008)

Electronic Communications in Probability [electronic only]

On the Sharpness of Some Upper Bounds for the Spectral Radii of S.O.R. Iteration Matrices.

R.S. Varga, M. Neumann (1980)

Numerische Mathematik

On the singular graph and the Weyr characteristic of an M-matrix.

Hans Schneider, D.J. Richman (1978)

Aequationes mathematicae

On the singular values of random matrices

Shahar Mendelson, Grigoris Paouris (2014)

Journal of the European Mathematical Society

We present an approach that allows one to bound the largest and smallest singular values of an $N \times n$ random matrix with iid rows, distributed according to a measure on $ℝ^{n}$ that is supported in a relatively small ball and linear functionals are uniformly bounded in $L_{p}$ for some $p > 8$ , in a quantitative (non-asymptotic) fashion. Among the outcomes of this approach are optimal estimates of $1 \pm c \sqrt{n / N}$ not only in the case of the above mentioned measure, but also when the measure is log-concave or when it a product measure...

On the span invariant for cubic similarity

Gianluca Gorni, Halszka Tutaj-Gasińska (2001)

Annales Polonici Mathematici

Given a real n×n matrix A, we make some conjectures and prove partial results about the range of the function that maps the n-tuple x into the entrywise kth power of the n-tuple Ax. This is of interest in the study of the Jacobian Conjecture.

On the special trace decomposition problem on quaternion structure.

Lakomá, Lenka, Mikes̆, Josef (1997)

General Mathematics

On the spectral norm of a random Toeplitz matrix.

Meckes, Mark W. (2007)

Electronic Communications in Probability [electronic only]

On the star partial ordering of normal matrices.

Merikoski, Jorma K., Liu, Xiaoji (2006)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

On the structure of positive maps between matrix algebras

Władysław A. Majewski, Marcin Marciniak (2007)

Banach Center Publications

The structure of the set of positive unital maps between M₂(ℂ) and Mₙ(ℂ) (n ≥ 3) is investigated. We proceed with the study of the "quantized" Choi matrix thus extending the methods of our previous paper [MM2]. In particular, we examine the quantized version of Størmer's extremality condition. Maps fulfilling this condition are characterized. To illustrate our approach, a careful analysis of Tang's maps is given.

On the volume of the double stochastic matrices.

Schmuckenschläger, M. (1992)

Acta Mathematica Universitatis Comenianae. New Series

On the volume of the polytope of doubly stochastic matrices.

Chan, Clara S., Robbins, David P. (1999)

Experimental Mathematics

On the weak robustness of fuzzy matrices

Ján Plavka (2013)

Kybernetika

A matrix $A$ in $(max, min)$ -algebra (fuzzy matrix) is called weakly robust if $A^{k} \otimes x$ is an eigenvector of $A$ only if $x$ is an eigenvector of $A$ . The weak robustness of fuzzy matrices are studied and its properties are proved. A characterization of the weak robustness of fuzzy matrices is presented and an $O (n^{2})$ algorithm for checking the weak robustness is described.

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