Related papers: It\'eration d'applications rationnelles dans les e…
In this paper, we use elementary method to give a classification of the multiplicative maps on matrix algebra $M_{n}(\mF)$ over a field $\mF$ of characteristic $0$. All the multiplicative maps are classified into three classes: the trivial…
The rational Landen transformation is a map on the space of coefficients of a rational integrand that preserves the value of the integral. We provide a family of these transformations that apply to rational integrands on the whole line.…
We study the differential and metric structures of the set of real square roots of a non-singular real matrix, under the assumption that the matrix and its square roots are semi-simple, or symmetric, or orthogonal.
This note will discuss the dynamics of iterated cubic maps from the real or complex line to itself, and will describe the geography of the parameter space for such maps. It is a rough survey with few precise statements or proofs, and…
We construct a family of iterations for computing the principal square root of a square matrix $A$ using Zolotarev's rational minimax approximants of the square root function. We show that these rational functions obey a recursion, allowing…
Let $n$ and $s$ be fixed integers such that $n\geq 2$ and $1\leq s\leq \frac{n}{2}$. Let $M_n(\mathbb{K})$ be the ring of all $n\times n$ matrices over a field $\mathbb{K}$. If a map $\delta:M_n(\mathbb{K})\rightarrow M_n(\mathbb{K})$…
Modeling of multidimensional signal using tensor is more convincing than representing it as a collection of matrices. The tensor based approaches can explore the abundant spatial and temporal structures of the mutlidimensional signal. The…
The theory of positive maps plays a central role in operator algebras and functional analysis, and has countless applications in quantum information science. The theory was originally developed for operators acting on complex Hilbert…
The Fatou-Julia theory for rational functions has been extended both to transcendental meromorphic functions and more recently to several different types of quasiregular mappings in higher dimensions. We extend the iterative theory to…
This paper proposes a unique optimization approach for estimating the minimax rational approximation and its application for evaluating matrix functions. Our method enables the extension to generalized rational approximations and has the…
The article is devoted to different aspects of the question "What can be done with a matrix by low rank perturbation?" It is proved that one can change a geometrically simple spectrum drastically by a rank 1 permutation, but the situation…
One considers the behavior of the degree of a rational map under specialization of the coefficients of the defining linear system. The method rests on the classical idea of Kronecker as applied to the context of projective schemes and their…
The geometry of rotations in dimensions 3, 4, and 5 is discussed using the matrix exponential map. Explicit closed formulas for the exponential of an antisymmetric matrix, as well as the logarithm of a rotation, are given for these…
In this paper we give different compactifications for the domain and the codomain of an affine rational map $f$ which parametrizes a hypersurface. We show that the closure of the image of this map (with possibly some other extra…
Decision making under uncertainty is a cross-cutting challenge in science and engineering. Most approaches to this challenge employ probabilistic representations of uncertainty. In complicated systems accessible only via data or black-box…
This chapter deepens cartographic communication through a cartographic multirepresentation exercise. Using a single dataset on World population data, the chapter presents a series of 13 different maps to illustrate how mapping is primarily…
We give formulas and effective sharp bounds for the degree of multi-graded rational maps and provide some effective and computable criteria for birationality in terms of their algebraic and geometric properties. We also extend the Jacobian…
Polynomial minimal bases of rational vector subspaces are a classical concept that plays an important role in control theory, linear systems theory, and coding theory. It is a common practice to arrange the vectors of any minimal basis as…
Using linear algebra methods we study certain algebraic properties of monomial rings and matroids. Let I be a monomial ideal in a polynomial ring over an arbitrary field. If the Rees cone of I is quasi-ideal, we express the normalization of…
We consider mappings satisfying an upper bound for the distortion of families of curves. We establish lower bounds for the distortion of distances under such mappings. As applications, we obtain theorems on the discreteness of the limit…