Related papers: Every matrix is a product of Toeplitz matrices
In the last decade, a large amount of research has been concentrated on the operators living on the model space. Asymmetric truncated Toeplitz operators and asymmetric truncated Hankel operators are the natural generalization of truncated…
We prove Nehari's theorem for integral Hankel and Toeplitz operators on simple convex polytopes in several variables. A special case of the theorem, generalizing the boundedness criterion of the Hankel and Toeplitz operators on the…
We introduce a linear-time algorithm for computing the Frobenius normal form (FNF) of symmetric Toeplitz matrices by utilizing their inherent structural properties through a graph-theoretic approach. Previous results of the authors…
Patterned random matrices such as the reverse circulant, the symmetric circulant, the Toeplitz and the Hankel matrices and their almost sure limiting spectral distribution (LSD), have attracted much attention. Under the assumption that the…
The determination of the density functions for products of random elements from specified classes of matrices is a basic problem in random matrix theory and is also of interest in theoretical physics. For connected simple Lie groups of…
Toeplitz matrices are ubiquitous and play important roles across many areas of mathematics. In this paper, we present some algebraic results concerning block Toeplitz matrices with block entries belonging to a commutative algebra $\AA$. The…
Let k be a field, n a positive integer, X a generic nxn matrix over k (i.e., a matrix (x_{ij}) of n^2 independent indeterminates over the polynomial ring k[x_{ij}]), and adj(X) its classical adjoint. It is shown that if char k=0 and n is…
Taking the product of (2n+1)/(2n+2) raised to the power +1 or -1 according to the n-th term of the Thue-Morse sequence gives rise to an infinite product P while replacing (2n+1)/(2n+2) with (2n)/(2n+1) yields an infinite product Q, where P…
The paper deals with the invertibility of Toeplitz plus Hankel operators T(a)+H(b) acting on classical Hardy spaces on the unit circle T. It is supposed that the generating functions a and b satisfy the condition a(t)a(1/t)=b(t)b(1/t).…
One tuple of probability vectors is more informative than another tuple when there exists a single stochastic matrix transforming the probability vectors of the first tuple into the probability vectors of the other. This is called matrix…
The authors of the title proved an elegant identity expressing a Toeplitz determinant in terms of the Fredholm determinant of an infinite matrix which (although not described as such) is the product of two Hankel matrices. The proof used…
We obtain several rigidity results regarding tensor product decompositions of factors. First, we show that any full factor with separable predual has at most countably many tensor product decompositions up to stable unitary conjugacy. We…
Bernstein polynomials, long a staple of approximation theory and computational geometry, have also increasingly become of interest in finite element methods. Many fundamental problems in interpolation and approximation give rise to…
The maximal algebras of scalar Toeplitz matrices are known to be formed by generalized circulants. The identification of algebras consisting of block Toeplitz matrices is a harder problem, that has received little attention up to now. We…
In contrast to the situation in classical linear algebra, not every tropically non-singular matrix can be factored into a product of tropical elementary matrices. We do prove the factorizability of any tropically non-singular 2x2 matrix…
Compound matrices play an important role in many fields of mathematics and have recently found new applications in systems and control theory. However, the explicit formulas for these compounds are non-trivial and not always easy to use.…
We consider the set $\mathcal{M}_n(\mathbb Z; H)$ of $n\times n$-matrices with integer elements of size at most $H$ and obtain a new upper bound on the number of matrices from $\mathcal{M}_n(\mathbb Z; H)$ with a given characteristic…
We study the problem of when a periodic square matrix of order $n$ over an arbitrary field $\mathbb{F}$ is decomposable into the sum of a square-zero matrix and a torsion matrix, and show that this decomposition can always be obtained for…
We give a characterization of compact and Fredholm operators on polyanalytic Fock spaces in terms of limit operators. As an application we obtain a generalization of the Bauer-Isralowitz theorem using a matrix valued Berezin type transform.…
It is widely known that the lower bound for the algorithmic complexity of square matrix multiplication resorts to at least $n^2$ arithmetic operations. The justification builds upon the following reasoning: given that there are $2 n^2$…