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Displaying 1601 – 1620 of 2599

On the limiting empirical measure of eigenvalues of the sum of rank one matrices with log-concave distribution

A. Pajor, L. Pastur (2009)

Studia Mathematica

We consider n × n real symmetric and hermitian random matrices Hₙ that are sums of a non-random matrix $H ₙ^{(0)}$ and of mₙ rank-one matrices determined by i.i.d. isotropic random vectors with log-concave probability law and real amplitudes. This is an analog of the setting of Marchenko and Pastur [Mat. Sb. 72 (1967)]. We prove that if mₙ/n → c ∈ [0,∞) as n → ∞, and the distribution of eigenvalues of $H ₙ^{(0)}$ and the distribution of amplitudes converge weakly, then the distribution of eigenvalues of Hₙ converges...

On the linear capacity of algebraic cones

Marcin Skrzyński (2002)

Mathematica Bohemica

We define the linear capacity of an algebraic cone, give basic properties of the notion and new formulations of certain known results of the Matrix Theory. We derive in an explicit way the formula for the linear capacity of an irreducible component of the zero cone of a quadratic form over an algebraically closed field. We also give a formula for the linear capacity of the cone over the conjugacy class of a “generic” non-nilpotent matrix.

On the linearized stability of age-structured multispecies populations.

Farkas, Jozsef Z. (2006)

Journal of Applied Mathematics

On the lower bound of the spectral norm of symmetric random matrices with independent entries.

Péché, Sandrine, Soshnikov, Alexander (2008)

Electronic Communications in Probability [electronic only]

On the LU Factorization of M-Matrices.

R.S. Varga, D.Y. Cai (1982)

Numerische Mathematik

On the $m$ -th roots of a complex matrix.

Psarrakos, Panayiotis J. (2002)

ELA. The Electronic Journal of Linear Algebra [electronic only]

On the matrices of central linear mappings

Hans Havlicek (1996)

Mathematica Bohemica

We show that a central linear mapping of a projectively embedded Euclidean $n$ -space onto a projectively embedded Euclidean $m$ -space is decomposable into a central projection followed by a similarity if, and only if, the least singular value of a certain matrix has multiplicity $\geq 2 m - n + 1$ . This matrix is arising, by a simple manipulation, from a matrix describing the given mapping in terms of homogeneous Cartesian coordinates.

On the matrix equation $x^{n} = B$ over finite fields.

Acosta-de-Orozco, Maria T., Gomez-Calderon, Javier (1993)

International Journal of Mathematics and Mathematical Sciences

On the matrix negative Pell equation

Aleksander Grytczuk, Izabela Kurzydło (2009)

Discussiones Mathematicae - General Algebra and Applications

Let N be a set of natural numbers and Z be a set of integers. Let M₂(Z) denotes the set of all 2x2 matrices with integer entries. We give necessary and suficient conditions for solvability of the matrix negative Pell equation (P) X² - dY² = -I with d ∈ N for nonsingular X,Y belonging to M₂(Z) and his generalization (Pn) $\sum_{i = 1}^{n} X ₂_{i} - d \sum_{i = 1}^{n} Y ²_{i} = - I$ with d ∈ N for nonsingular $X_{i}, Y_{i} \in M ₂ (Z)$ , i=1,...,n.