Related papers: Bilinear matrix inequalities and polynomials in se…
In a previous paper, we have given an algebraic model to the set of intervals. Here, we apply this model in a linear frame. We define a notion of diagonalization of square matrices whose coefficients are intervals. But in this case, with…
We prove that polynomial valuations on vector lattices correspond to orthosymmetric multilinear maps. As a consequence we obtain a concise proof of the equivalence of orthosymmetry and orthogonal additivity.
The problem of minimizing a multilinear function of binary variables is a well-studied NP-hard problem. The set of solutions of the standard linearization of this problem is called the multilinear set. We study a cardinality constrained…
Properties of 2-adic valuation sequences for general quadratic polynomials with integer coefficients are determined directly from the coefficients. These properties include boundedness or unboundedness, periodicity, and valuations at…
A commutative associative algebra A with an identity over the field of real numbers which has a basis, where all elements are invertible, is considered in the work. Moreover, among matrixes consisting of the structure constants of A, there…
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…
When doubly-affine matrices such as Latin and magic squares with a single non-zero eigenvalue are powered up they become constant matrices after a few steps. The process of compounding squares of orders m and n can then be used to generate…
We study multivariate normal models that are described by linear constraints on the inverse of the covariance matrix. Maximum likelihood estimation for such models leads to the problem of maximizing the determinant function over a…
The observational characteristics of a linear structural equation model can be effectively described by polynomial constraints on the observed covariance matrix. However, these polynomials can be exponentially large, making them impractical…
In this note functions that transform open segments of a linear space into open segments of another linear space are studied and characterized. Assuming that the range is non-collinear, it is proved that such a map can always be expressed…
We show the existence of polynomial maps which have a regular bifurcation value, while over a neighbourhood of this value the fibres are connected and diffeomorphic.
A minimal homogeneous generating system of the algebra of semi-invariants of tuples of two-by-two matrices over an infinite field of characteristic two or over the ring of integers is given. In an alternative interpretation this yields a…
This paper introduces and develops the algebraic framework of moment polynomials, which are polynomial expressions in commuting variables and their formal mixed moments. Their positivity and optimization over probability measures supported…
A unified theory of orthogonal polynomials of a discrete variable is presented through the eigenvalue problem of hermitian matrices of finite or infinite dimensions. It can be considered as a matrix version of exactly solvable Schr\"odinger…
This is a straightforward introduction to the properties of polynomials in many variables that do not vanish in the open upper half plane. Such polynomials generalize many of the well-known properties of polynomials with all real roots.
We present a concentration inequality for linear functionals of noncommutative polynomials in random matrices. Our hypotheses cover most standard ensembles, including Gaussian matrices, matrices with independent uniformly bounded entries…
Let $f(x_1,...,x_k)$ be a polynomial over a field $K$. This paper considers such questions as the enumeration of the number of nonzero coefficients of $f$ or of the number of coefficients equal to $\alpha\in K^*$. For instance, if $K=\ff_q$…
Let $K$ be a field, $R=K[x, y]$ the polynomial ring and $\mathcal{M}(K)$ the set of all pairs of square matrices of the same size over $K.$ Pairs $P_1=(A_1,B_1)$ and $P_2=(A_2,B_2)$ from $\mathcal{M}(K)$ are called similar if…
A nonstandard application of bivariate polynomial interpolation is discussed: the implicitization of a rational algebraic curve given by its parametric equations. Three different approaches using the same interpolation space are considered,…
A univariate trace polynomial is a polynomial in a variable x and formal trace symbols Tr(x^j). Such an expression can be naturally evaluated on matrices, where the trace symbols are evaluated as normalized traces. This paper addresses…