Related papers: A Criterion for the Covering Condition of Generali…
In this paper we consider the electromagnetic scattering problem by an obstacle characterised by a Generalized Impedance Boundary Condition in the harmonic regime. These boundary conditions are well known to provide accurate models for thin…
In this technical note, cluster consensus of discrete-time linear multi-agent systems is investigated. A set of stochastic matrices $\mathcal{P}$ is said to be a cluster consensus set if the system achieves cluster consensus for any initial…
We introduce a new class of large structured random matrices characterized by four fundamental properties which we discuss. We prove that this class is stable under matrix-valued and pointwise non-linear operations. We then formulate an…
We propose a range criterion which is a sufficient and necessary condition satisfied by two pure states transformable with each other under reversible stochastic local operations assisted with classical communication. We also provide a…
We survey some recent progress on rigorously establishing the universality of various spectral statistics of Wigner random matrix ensembles, focusing in particular on the Four Moment Theorem and its applications.
Random linear systems over the Galois Field modulo 2 have an interest in connection with problems ranging from computational optimization to complex networks. They are often approached using random matrices with Poisson-distributed or…
Neighborhood is an important concept in covering based rough sets. That under what condition neighborhoods form a partition is a meaningful issue induced by this concept. Many scholars have paid attention to this issue and presented some…
We describe Generalized Hermitian matrices ensemble sometimes called Chiral ensemble. We give global asymptotic of the density of eigenvalues or the statistical density. We will calculate a Laplace transform of such a density for finite…
A matrix completion problem is to recover the missing entries in a partially observed matrix. Most of the existing matrix completion methods assume a low rank structure of the underlying complete matrix. In this paper, we introduce an…
The necessary and suffcient condition for a set of matrices to commute is given and proven.
We verify a conjecture on the structure of higher-rank numerical ranges for a wide class of unitary and normal matrices. Using analytic and geometric techniques, we show precisely how the higher-rank numerical ranges for a generic unitary…
We investigate the eigenvalues statistics of ensembles of normal random matrices when their order N tends to infinite. In the model the eigenvalues have uniform density within a region determined by a simple analytic polynomial curve. We…
In this paper, we determine the sharp threshold for universality of cokernels of random matrices over finite fields. More precisely, we prove the following: given any constant $c>1$, let $A(n)$ be a random $n \times n$ matrix over…
The standard theorem for regular stochastic matrices is generalized to matrices with no sign restriction on the entries. The condition that column sums be equal to 1 is kept, but the regularity condition is replaced by a condition on the…
We consider level crossing in a matrix family $H=H_0+\lambda V$ where $H_0$ is a fixed $N\times N$ matrix and $V$ belongs to one of the standard Gaussian random matrix ensembles. We study the probability distribution of level crossing…
In this paper we enumerate the parameter matrices of all perfect 2-colorings of the generalized Petersen graphs GP(n;3), where n>=7. We also give some basic results for GP(n; k).
This paper proposes a simple yet powerful ensemble classifier, called Random Hyperboxes, constructed from individual hyperbox-based classifiers trained on the random subsets of sample and feature spaces of the training set. We also show a…
Some tools and ideas are interchanged between random matrix theory and multivariate statistics. In the context of the random matrix theory, classes of spherical and generalised Wishart random matrix ensemble, containing as particular cases…
Matrix conditions extend linear Mal'tsev conditions from Universal Algebra to exactness properties in Category Theory. Some can be stated in the finitely complete context while, in general, they can only be stated for regular categories. We…
In this article we prove a necessary and a sufficient condition for a finite subset of the special linear group to be dominated. These conditions are purely geometric in nature, as they only involve the trace and the eigenvectors of the…