Related papers: Groups of matrices with approximately submultiplic…
We study matrix semigroups in which ring commutators have real spectra. We prove that irreducible semigroups with this property are simultaneously similar to semigroups of real-entried matrices. We also obtain a structure theorem for…
If a tuple of matrices has a common invariant subspace, its projective joint spectrum has an algebraic component. In general, the converse is not true, and there might be algebraic components in the projective joint spectrum without…
In the paper, a simple condition guaranteing the finiteness property for a bounded set of matrices is presented. Given a bounded set S of real or complex matrices, it is shown that existence of a sequence of matrix products such that the…
The equational probabilistic spectrum of a finite algebra is the set of probabilities with which equations are satisfied in the algebra. We study algebras with minimal spectrum, that is, spectra consisting only of the values $1$ and…
We obtain sequences of inclusion sets for the spectrum, essential spectrum, and pseudospectrum of banded, in general non-normal, matrices of finite or infinite size. Each inclusion set is the union of the pseudospectra of certain…
Let A be a singular matrix of M_n(K), where K is an arbitrary field. Using canonical forms, we give a new proof that the sub-semigroup of (M_n(K),x) generated by the similarity class of A is the set of matrices of M_n(K) with a rank lesser…
We compute spectra of symmetric random matrices defined on graphs exhibiting a modular structure. Modules are initially introduced as fully connected sub-units of a graph. By contrast, inter-module connectivity is taken to be incomplete.…
We study the spectra of non-regular semisimple elements in irreducible representations of simple algebraic groups. More precisely, we prove that if G is a simply connected simple linear algebraic group and f is a non-trivial irreducible…
This note deals with a simultaneous approximation of several matrices by a finite family of diagonalizable matrices satisfying an additional condition for the spectrum of a matrix product. That is the simplicity of all eigenvalues.
We prove that, in both real and complex cases, there exists a pair of matrices that generates a dense subsemigroup of the set of $n\times n$ matrices.
Patterns on numerical semigroups are multivariate linear polynomials, and they are said to be admissible if there exists a numerical semigroup such that evaluated at any nonincreasing sequence of elements of the semigroup gives integers…
We consider certain matrix-products where successive matrices in the product belong alternately to a particular qualitative class or its transpose. The main theorems relate structural and spectral properties of these matrix-products to the…
In this paper, we define the adjacency matrix of a semigraph. We give the conditions for a matrix to be semigraphical and give an algorithm to construct a semigraph from the semigraphical matrices. We derive lower and upper bounds for…
Recently, several research efforts showed that the analysis of joint spectral characteristics of sets of matrices is greatly eased when these matrices share an invariant cone. In this short note we prove two new results in this direction.…
In this paper, a new class of band matrices is considered where the entries of each non-zero band form a sequence with two limit points. The compact perturbation technique is used to study the spectrum over the $\ell_{p}, (1<p<\infty)$…
An irreducible norm closed semigroup of complex matrices is simultaneously similar to a semigroup of partial isometries if and only if (a) the norms of all nonzero members of it are uniformly bounded above and below, and (b) its idempotents…
We estimate the size of the spectral gap at zero for some Hermitian block matrices. Included are quasi-definite matrices, quasi-semidefinite matrices (the closure of the set of the quasi-definite matrices) and some related block matrices…
We study abstract finite groups with the property, called property $\hat{s}$, that all of their subrepresentations have submultiplicative spectra. Such groups are necessarily nilpotent and we focus on $p$-groups. $p$-groups with property…
The semi-tensor product (STP) of matrices is extended to the STP of hypermatrices. Some basic properties of the STP of matrices are extended to the STP of hypermatrices. The hyperdeterminant of hypersquares is introduced. Some algebraic and…
It is known that semi-magic square matrices form a 2-graded algebra or superalgebra with the even and odd subspaces under centre-point reflection symmetry as the two components. We show that other symmetries which have been studied for…