Related papers: Linear relations and their singular chains
Line congruences are $2$-dimensional families of lines in $3$-space. The singularities that appear in generic line congruences are folds, cusps and swallowtails. In this paper we give a geometric description of these singularities. The main…
We investigate point-line geometries whose singular subspaces correspond to binary equidistant codes. The main result is a description of automorphisms of these geometries. In some important cases, automorphisms induced by non-monomial…
Large-scale eigenvalue problems arise in various fields of science and engineering and demand computationally efficient solutions. In this study, we investigate the subspace approximation for parametric linear eigenvalue problems, aiming to…
We extend the concept of eigenvector centrality to multiplex networks, and introduce several alternative parameters that quantify the importance of nodes in a multi-layered networked system, including the definition of vectorial-type…
Our goal here is to see the space of matrices of a given size from a geometric and topological perspective, with emphasis on the families of various ranks and how they fit together. We pay special attention to the nearest orthogonal…
Characterizing the importances (i.e., centralities) of nodes in social, biological, and technological networks is a core topic in both network science and data science. We present a linear-algebraic framework that generalizes…
It is well-known that the controllability of finite-dimensional nonlinear systems can be established by showing the controllability of the linearized system. However, this classical result does not generalize to infinite-dimensional…
The general correlation function for the eigenvalues of $p$ complex hermitian matrices coupled in a chain is given as a single determinant. For this we use a slight generalization of a theorem of Dyson.
In a previous paper, we have given an algebraic model to the set of intervals. Here, we apply this model in a linear frame. We define a notion of diagonalization of square matrices whose coefficients are intervals. But in this case, with…
A lot of information concerning solutions of linear differential equations can be computed directly from the equation. It is therefore natural to consider these equations as a data-structure, from which mathematical properties can be…
This document presents a series of open questions arising in matrix computations, i.e., the numerical solution of linear algebra problems. It is a result of working groups at the workshop Linear Systems and Eigenvalue Problems, which was…
The term interlacing refers to systematic inequalities between the sequences of eigenvalues of two operators defined on objects related by a specific oper- ation. In particular, knowledge of the spectrum of one of the objects then implies…
The dimensions of sets of matrices of various types, with specified eigenvalue multiplicities, are determined. The dimensions of the sets of matrices with given Jordan form and with given singular value multiplicities are also found. Each…
We apply a recently proposed definition of a linear connection in non commutative geometry based on the natural bimodule structure of the algebra of differential forms to the case of the two-parameter quantum plane. We find that there…
Let $f(x)$ be a monic polynomial over $\mathbb{Q}$ with complex roots $\alpha_1,\dots,\alpha_n$. Linear relations among them and $1$ over $\mathbb{Q}$ play an important role when we study the distribution of roots modulo a prime. We study…
In this work, firstly the maximal sectorial linear relations are described. Later on, the discreteness of the spectrum of the linear maximal sectorial operators and asymptotical behaviour of the eigenvalues of such operators in terms of the…
The paper is devoted to developing subdifferential theory for set-valued mappings taking values in ordered infinite-dimensional spaces. This study is motivated by applications to problems of vector and set optimization with various…
We develop the theory of equiangular lines in Euclidean spaces. Our focus is on the question of when a Seidel matrix having precisely three distinct eigenvalues has a regular graph in its switching class. We make some progress towards an…
A scalar integer partition problem asks for a number of nonnegative integer solutions to a linear Diophantine equation with integer positive coefficients. The manuscript discusses an algorithm of derivation of linear relations involving the…
Optical singularities, which are positions within an electromagnetic field where certain field parameters become undefined, hold significant potential for applications in areas such as super-resolution microscopy, sensing, and…