Related papers: Integer matrices that are not copositive have cert…

We address the issue of establishing standard forms for nonnegative and Metzler matrices by considering their similarity to nonnegative and Metzler Hessenberg matrices. It is shown that for dimensions $n \geq 3$, there always exists a…

A positive definite symmetric matrix {\sigma} qualifies as a quantum mechanical covariance matrix if and only if {\sigma}+(1/2)i\hbar{\Omega}\geq0 where {\Omega} is the standard symplectic matrix. This well-known condition is a strong…

A $n\times n$ matrix $A$, which has a certain sign-symmetric structure ($J$--sign-symmetric), is studied in this paper. It is shown that such a matrix is similar to a nonnegative matrix. The existence of the second in modulus positive…

For matrices with all nonnegative entries, the Perron-Frobenius theorem guarantees the existence of an eigenvector with all nonnegative components. We show that the existence of such an eigenvector is also guaranteed for a very different…

We develop a general and unconditional framework for certifying the global nonnegativity of multivariate integer polynomials; based on rewriting them as sum of squares modulo their gradient ideals. We remove the two structural assumptions…

Any associative bilinear multiplication on the set of n-by-n matrices over some field of characteristic not two, that makes the same vectors orthogonal and has the same trace as ordinary matrix multiplication, must be ordinary matrix…

We consider infinite parametric families of high degree number fields composed of quadratic fields with pure cubic, pure quartic, pure sextic fields and with the so called simplest cubic, simplest quartic fields. We explicitly describe an…

We define a novel notion of ``non-backtracking'' matrix associated to any symmetric matrix, and we prove a ``Ihara-Bass'' type formula for it. We use this theory to prove new results on polynomial-time strong refutations of random…

In this article we develop new methods for exhibiting convex semialgebraic sets that are not spectrahedral shadows. We characterize when the set of nonnegative polynomials with a given support is a spectrahedral shadow in terms of sums of…

In this paper, we derive a general expression for mth powers of symmetric(0,1)-heptadiagonal matrices with n = 3k order,k = 1,2,3,...,n/3).

A real $n$-by-$n$ idempotent matrix $A$ with all entries having the same absolute value is called {\it absolutely flat}. We consider the possible ranks of such matrices and herein characterize the triples: size, constant, and rank for which…

If $A$ is an integer valued, strictly expansive matrix, then there exists an orthonormal $A$-wavelet whose Fourier transform is compactly supported and smooth. We show that strongly connected diagonally dominant integer matrices are…

For a real matrix $M$, we denote by $sp(M)$ the spectrum of $M$ and by $\left \vert M\right \vert $ its absolute value, that is the matrix obtained from $M$ by replacing each entry of $M$ by its absolute value. Let $A$ be a nonnegative real…

We show that for every subset $E$ of positive density in the set of integer square-matrices with zero traces, there exists an integer $k \geq 1$ such that the set of characteristic polynomials of matrices in $E-E$ contains the set of…

Given a real symmetric $n\times n$ matrix, the sepr-sequence $t_1\cdots t_n$ records information about the existence of principal minors of each order that are positive, negative, or zero. This paper extends the notion of the sepr-sequence…

In this paper we characterize the nonnegative irreducible tridiagonal matrices and their permutations, using certain entries in their primitive idempotents. Our main result is summarized as follows. Let $d$ denote a nonnegative integer. Let…

Let I=<f_1, ..., f_m> be a zero dimensional radical ideal Q[x_1,...,x_n]. Assume that we are given approximations {z_1,...,z_k} in C^n for the common roots V(I)={xi_1,...,xi_k}. In this paper we show how to construct and certify the…

A collection $\mathcal S$ of equivalence classes of positive definite integral quadratic forms in $n$ variables is called an $n$-exceptional set if there exists a positive definite integral quadratic form which represents all equivalence…

An n x n permutative matrix is a matrix in which every row is a permutation of the first row. In this paper the result given by Paparella in [Electron. J. Linear Algebra 31 (2016) 306-312] is extended to a more general lists of real and…

Let L be a restricted Lie superalgebra with its enveloping algebra u(L) over a field F of characteristic p>2. A polynomial identity is called non-matrix if it is not satisfied by the algebra of 2\times 2 matrices over F. We characterize L…