Related papers: Preserver problems on Toeplitz matrices

Szalai et al. (SIAM J. on Sci. Comp. 28(4), 2006) gave a general construction for characteristic matrices for systems of linear delay-differential equations with periodic coefficients. First, we show that matrices constructed in this way…

The purpose of this paper is to compute the asymptotics of determinants of finite sections of operators that are trace class perturbations of Toeplitz operators. For example, we consider the asymptotics in the case where the matrices are of…

We study Toeplitz operators with respect to a commuting $n$-tuple of bounded operators which satisfies some additional conditions coming from complex geometry. Then we consider a particular such tuple on a function space. The algebra of…

We discuss resent developments in the problem of description of finite rank Toeplitz operators in different Bergman spaces and give some applications in analysis and mathematical physics

The category of Hilbert spaces and contractions has filtered colimits, and tensoring preserves them. We also discuss (problems with) bounded maps.

Numerical computations involving rational matrices often benefit from preserving underlying matrix structures such as symmetry, Hermitian properties, or sparsity that reflect physical, geometric, or algebraic characteristics of the system.…

This paper studies the spectral properties of large matrices and the preconditioning of linear systems, arising from the finite difference discretization of a time-dependent space-fractional diffusion equation with a variable coefficient…

These notes concern linear transformations on R^n and C^n, exponentials of linear transformations, and some related geometric questions.

A manifestly covariant equation is derived to describe the second order perturbations in topological defects and membranes on arbitrary curved background spacetimes. This, on one hand, generalizes work on macroscopic strings in Minkowski…

We determine the group of linear transformations on a vector space $V$ that preserve a polynomial function $f$ on $V$ for several interesting pairs $(V,f)$, using the theory of semisimple algebraic groups.

In this paper we expose our main results about rank problems concerning persymmetric matrices over F_2 associated to some exponential sums.

In this paper first we give a partial answer to a question of L. Moln\'ar and W. Timmermann. Namely, we will describe those linear (not necessarily bijective) transformations on the set of self-adjoint matrices which preserve a unitarily…

Let $\mathcal H$ be a complex Hilbert space and $\mathcal F_s (\mathcal H)$ the real vector space of all self-adjoint finite rank bounded operators on $\mathcal H$. We generalize the famous Wigner's theorem by characterizing linear maps on…

Let K be an arbitrary (commutative) field, and V be a linear subspace of M_n(K) such that codim V<n-1. Using a recent generalization of a theorem of Atkinson and Lloyd, we show that every linear embedding of V into M_n(K) which strongly…

We introduce and give a more or less complete study of a family of branching-Toeplitz operators on the Hilbert space $\ell^2(T_q)$ indexed by a rooted homogeneous tree $T_q$ of degree $q\ge 2$. The finite dimensional analogues of such…

Matrices are typically considered over fields or rings. Motivated by applications in parametric differential equations and data-driven modeling, we suggest to study matrices with entries from a Hilbert space and present an elementary theory…

This paper is concerned with the distance of a symmetric tridiagonal Toeplitz matrix $T$ to the variety of similarly structured singular matrices, and with determining the closest matrix to $T$ in this variety. Explicit formulas are…

We study the structure of isometries defined on the algebra $\mathcal{A}$ of upper-triangular Toeplitz matrices. Our first result is that a continuous multiplicative isometry $\mathcal{A}\to M_n$ must be of the form either $A\mapsto UAU^*$…

In this paper, we consider the rank-one tensor completion problem. We address the question of existence and uniqueness of the rank-one solution. In particular we show that the global uniqueness over the field of real numbers can be verified…

We show that two tensor permutation matrices permutate tensor product of rectangle matrices. Some examples, in the particular case of tensor commutation matrices, for studying some linear matrix equations are given.