Related papers: Analytic mappings between noncommutative pencil ba…

We study the images of polynomial maps over algebraically closed division rings. Our first result generalizes the classical Ax-Grothendieck theorem: We show that if $ f_1, \ldots, f_m $ are elements of the free associative algebra $…

In this paper, we studied the map defined by a non-very ample line bundle on some special irregular varieties. As to this topic, it is well known that for a line bundle $L$ on an Abelian variety $A$, the linear system $|2L|$ is base point…

Let $p$ be a polynomial in several non-commuting variables with coefficients in a field $K$ of arbitrary characteristic. It has been conjectured that for any $n$, for $p$ multilinear, the image of $p$ evaluated on the set $M_n(K)$ of $n$ by…

A matrix-valued measure $\Theta$ reduces to measures of smaller size if there exists a constant invertible matrix $M$ such that $M\Theta M^*$ is block diagonal. Equivalently, the real vector space ${\mathscr A}$ of all matrices $T$ such…

The nonnegative rank of a nonnegative matrix is the minimum number of nonnegative rank-one factors needed to reconstruct it exactly. The problem of determining this rank and computing the corresponding nonnegative factors is difficult;…

This paper is devoted to the study of perturbations of a matrix pencil, structured or unstructured, such that a perturbed pencil will reproduce a given deflating pair while maintaining the invariance of the complementary deflating pair. If…

The 4-dimensional Sklyanin algebra is the homogeneous coordinate ring of a noncommutative analogue of projective 3-space. The degree-two component of the algebra contains a 2-dimensional subspace of central elements. The zero loci of those…

Using representations of functional data can be more convenient and beneficial in subsequent statistical models than direct observations. These representations, in a lower-dimensional space, extract and compress information from individual…

Recent innovations on the differential calculus for functions of non-commuting variables, begun for a quaternionic variable, are now extended to the case of a general matrix over the complex numbers. The expansion of F(X+Delta) is given to…

Convergence is a crucial issue in iterative algorithms. Damping is commonly employed to ensure the convergence of iterative algorithms. The conventional ways of damping are scalar-wise, and either heuristic or empirical. Recently, an…

We consider the linearization of the Dirichlet-to-Neumann (DN) map as a function of the potential. We show that it is injective at a real analytic potential for measurements made at an open subset of analyticity of the boundary. More…

The article concerns low-rank approximation of matrices generated by sampling a smooth function of two $m$-dimensional variables. We identify several misconceptions surrounding a claim that, for a specific class of analytic functions, such…

To analyze nonlinear dynamic systems, we developed a new technique based on the square matrix method. We propose this technique called the \convergence map" for generating particle stability diagrams similar to the frequency maps widely…

We introduce the notion of angular values for deterministic linear difference equations and random linear cocycles. We measure the principal angles between subspaces of fixed dimension as they evolve under nonautonomous or random linear…

We consider the estimation of the state transition matrix in vector autoregressive models, when time sequence data is limited but nonsequence steady-state data is abundant. To leverage both sources of data, we formulate the least squares…

Let $K\ < x_i\ >$ be the free associative algebra generated by a finite or countable number of variables $x_i$. The notion of "letterplace correspondence" introduced in [1,2] for the graded (two-sided) ideals of $K\ < x_i\ >$ is extended in…

This paper shows certain classes of metric spaces characterized by volume growth properties of balls can viewed as graphs with infinitesimal edges. Our approach is based on nonstandard analysis.

In this paper it is shown that a generalized circulant matrix underlies every weakly Coupled Map Lattice (CML), independently of the form of the coupling term. Therefore, this matrix will appear always perturbative methods are used to get…

A modification of the well-known step-by-step process for solving Nevanlinna-Pick problems in the class of $\bR_0$-functions gives rise to a linear pencil $H-\lambda J$, where $H$ and $J$ are Hermitian tridiagonal matrices. First, we show…

Recently, Kirkpatrick et al. [ALT 2019] and Fallat et al. [JMLR 2023] introduced non-clashing teaching and showed it is the most efficient machine teaching model satisfying the Goldman-Mathias collusion-avoidance criterion. A teaching map…