Distributions homogènes sur des espaces de matrices
Divisible ℤ-modules
In this article, we formalize the definition of divisible ℤ-module and its properties in the Mizar system [3]. We formally prove that any non-trivial divisible ℤ-modules are not finitely-generated.We introduce a divisible ℤ-module, equivalent to a vector space of a torsion-free ℤ-module with a coefficient ring ℚ. ℤ-modules are important for lattice problems, LLL (Lenstra, Lenstra and Lovász) base reduction algorithm [15], cryptographic systems with lattices [16] and coding theory [8].
Dodgon's determinant-evaluation rule proved by TWO-TIMING MEN and WOMEN.
D-optimal and highly D-efficient designs with non-negatively correlated observations
In this paper we consider D-optimal and highly D-efficient chemical balance weighing designs. The errors are assumed to be equally non-negatively correlated and to have equal variances. Some necessary and sufficient conditions under which a design is D*-optimal design (regular D-optimal design) are proved. It is also shown that in many cases D*-optimal design does not exist. In many of those cases the designs constructed by Masaro and Wong (2008) and some new designs are shown to be highly D-efficient....
D-optimal weighing designs for four and five objects.
Dunkl operators and canonical invariants of reflection groups.
Dynamical Systems for Rational Normal Curves.
Dynamics of doubly stochastic quadratic operators on a finite-dimensional simplex
The present paper focuses on the dynamics of doubly stochastic quadratic operators (d.s.q.o) on a finite-dimensional simplex. We prove that if a d.s.q.o. has no periodic points then the trajectory of any initial point inside the simplex is convergent. We show that if d.s.q.o. is not a permutation then it has no periodic points on the interior of the two dimensional (2D) simplex. We also show that this property fails in higher dimensions. In addition, the paper also discusses the dynamics classifications...
Edge matrices for the fundamental cone.
Efficient computation of enclosures for the exact solvents of a quadratic matrix equation.
Eigenspace decompositions with respect to symmetrized incidence mappings.
Eigenspace of a circulant max–min matrix
The eigenproblem of a circulant matrix in max-min algebra is investigated. Complete characterization of the eigenspace structure of a circulant matrix is given by describing all possible types of eigenvectors in detail.
Eigenspace of a three-dimensional max-Łukasiewicz fuzzy matrix
Eigenvectors of a fuzzy matrix correspond to stable states of a complex discrete-events system, characterized by a given transition matrix and fuzzy state vectors. Description of the eigenspace (set of all eigenvectors) for matrices in max-min or max-drast fuzzy algebra was presented in previous papers. In this paper the eigenspace of a three-dimensional fuzzy matrix in max-Łukasiewicz algebra is investigated. Necessary and sufficient conditions are shown under which the eigenspace restricted to...
Eigenvalue condition numbers and a formula of Burke, Lewis and Overton.
Eigenvalue distribution of certain ray patterns
In this paper, the eigenvalue distribution of complex matrices with certain ray patterns is investigated. Cyclically real ray patterns and ray patterns that are signature similar to real sign patterns are characterized, and their eigenvalue distribution is discussed. Among other results, the following classes of ray patterns are characterized: ray patterns that require eigenvalues along a fixed line in the complex plane, ray patterns that require eigenvalues symmetric about a fixed line, and ray...
Eigenvalue distribution of random matrices : some recent results
Eigenvalue frequency and consistent sign pattern matrices
Eigenvalue multiplicities of products of companion matrices.
Eigenvalues and eigenvectors for the quaternion matrices of degree two.
Eigenvalues and eigenvectors of some tridiagonal matrices with non-constant diagonal entries
We give explicit expressions for the eigenvalues and eigenvectors of some tridiagonal matrices with non-constant diagonal entries. Our techniques are based on the theory of recurrent sequences.