Related papers: Compound matrices in systems and control theory
The main goal of the paper is the discussion of a deeper interaction between matrix theory over polynomial rings over a field and typical methods of commutative algebra and related algebraic geometry. This is intended in the sense of…
Tilt models offer intuitive and clean definitions of complex systems in which particles are influenced by global control commands. Despite a wide range of applications, there has been almost no theoretical investigation into the associated…
These Notes deal with various areas of mathematics, and seek reciprocal combinations, explore mutual relations, ranging from abstract objects to problems in physics.
In this paper the main results in arXiv:0901.3179v3, related to the matrix representation of polynomial maps, are restated in traditional way of linear algebra assuming that variable vectors are presented as column vectors. Some new results…
In formation control, an ensemble of autonomous agents is required to stabilize at a given configuration in the plane, doing so while agents are allowed to observe only a subset of the ensemble. As such, formation control provides a rich…
Modular forms appear in many facets of mathematics, and have played important roles in geometry, mathematical physics, number theory, representation theory, topology, and other areas. Around 1994, motivated by technical issues in homotopy…
Analytic perturbation theory for matrices and operators is an immensely useful mathematical technique. Most elementary introductions to this method have their background in the physics literature, and quantum mechanics in particular. In…
Techniques for the evaluation of complex polynomials with one and two variables are introduced. Polynomials arise in may areas such as control systems, image and signal processing, coding theory, electrical networks, etc., and their…
We present applications of rectangular matrix models to various combinatorial problems, among which the enumeration of face-bicolored graphs with prescribed vertex degrees, and vertex-tricolored triangulations. We also mention possible…
Arithmetic combinatorics is often concerned with the problem of bounding the behaviour of arbitrary finite sets in a group or ring with respect to arithmetic operations such as addition or multiplication. Similarly, combinatorial geometry…
We present a concise survey of matrix completion methods and associated implementations of several fundamental algorithms. Our study covers both passive and adaptive strategies. We further illustrate the behavior of a simple adaptive…
Complexity is an interdisciplinary concept which, first of all, addresses the question of how order emerges out of randomness. For many reasons matrices provide a very practical and powerful tool in approaching and quantifying the related…
This paper studies geometric properties of the Iterated Matrix Multiplication polynomial and the hypersurface that it defines. We focus on geometric aspects that may be relevant for complexity theory such as the symmetry group of the…
Periodic orbits and cycles, respectively, play a significant role in discrete- and continuous-time dynamical systems (i.e. maps and flows). To succinctly describe their shifts when the system is applied perturbation, the notions of…
We construct an approximation to field theories on the noncommutative torus based on soliton projections and partial isometries which together form a matrix algebra of functions on the sum of two circles. The matrix quantum mechanics is…
Scientific paper is devoted to research of T-matrix - matrix of composite numbers 6h+1 v 6h-1 in special view, and to her application in number theory.
We study the problem of determining a matrix whose $k$th multiplicative compound is a prescribed matrix~$M$. The cardinality of the set of matrices whose $k$th multiplicative compound equals~$M$ is characterized in terms of $\rank(M)$. On…
Mathematical modelling is a cornerstone of computational biology. While mechanistic models might describe the interactions of interest of a system, they are often difficult to study. On the other hand, abstract models might capture key…
We present in this paper some fundamental tools for developing matrix analysis over the complex quaternion algebra. As applications, we consider generalized inverses, eigenvalues and eigenvectors, similarity, determinants of complex…
A vector-circulant matrix is a natural generalization of the classical circulant matrix and has applications in constructing additive codes. This article formulates the concept of a vector-circulant matrix over finite fields and gives an…