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Given a square complex matrix $A$, we tackle the problem of finding the nearest matrix with multiple eigenvalues or, equivalently when $A$ had distinct eigenvalues, the nearest defective matrix. To this goal, we extend the general framework…
We prove that if an $n\times n$ matrix defined over ${\mathbb Q}_p$ (or more generally an arbitrary complete, discretely-valued, non-Archimedean field) satisfies a certain congruence property, then it has a strictly maximal eigenvalue in…
We prove that a bounded operator $T$ on a separable Banach space $X$ satisfying a strong form of the Frequent Hypercyclicity Criterion (which implies in particular that the operator is universal in the sense of Glasner and Weiss) admits…
The integrability condition called shape invariance is shown to have an underlying algebraic structure and the associated Lie algebras are identified. These shape-invariance algebras transform the parameters of the potentials such as…
We study the computational model where we can access a matrix $\mathbf{A}$ only by computing matrix-vector products $\mathbf{A}\mathrm{x}$ for vectors of the form $\mathrm{x} = \mathrm{x}_1 \otimes \cdots \otimes \mathrm{x}_q$. We prove…
The Semialgebraic Orbit Problem is a fundamental reachability question that arises in the analysis of discrete-time linear dynamical systems such as automata, Markov chains, recurrence sequences, and linear while loops. An instance of the…
We prove that the matrix of capacitance in electrostatics is a positive-singular matrix with a non-degenerate null eigenvalue. We explore the physical implications of this fact, and study the physical meaning of the eigenvalue problem for…
In this work we study the stability of the four vector irreducible pieces of the torsion and the nonmetricity tensors in the general quadratic metric-affine Lagrangian in 4 dimensions. The goal will be to elucidate under which conditions…
A recent problem in dynamics is to determinate whether an attractor $\Lambda$ of a $C^r$ flow $X$ is $C^r$ robust transitive or not. By {\em attractor} we mean a transitive set to which all positive orbits close to it converge. An attractor…
A ring is rigid if there is no nonzero locally nilpotent derivation on it. In terms of algebraic geometry, a rigid coordinate ring corresponds to an algebraic affine variety which does not allow any nontrivial algebraic additive group…
An interval matrix is a matrix whose entries are intervals in the set of real numbers. Let $p , q $ be nonzero natural numbers and let $\mu =( [m_{i,j}, M_{i,j}])_{i,j}$ be a $p \times q$ interval matrix; given a $p \times q$ matrix $A$…
The paper is devoted to the investigation of finite dimensional commutative nilpotent (associative) algebras N over an arbitrary base field of characteristic zero. Due to the lack of a general structure theory for algebras of this type (as…
The positive stability and D-stability of singular M-matrices, perturbed by (non-trivial) nonnegative rank one perturbations, is investigated. In special cases positive stability or D-stability can be established. In full generality this is…
We study the combinatorial and algebraic properties of Nonnegative Matrices. Our results are divided into three different categories. 1. We show a quantitative generalization of the 100 year-old Perron-Frobenius theorem, a fundamental…
We study the meet irreducible ideals in certain direct limit algebras, namely the strongly maximal triangular subalgebras of AF C*-algebras. These ideals have a description in terms of the coordinates, or spectrum, that is a natural…
Admissible vectors lead to frames or coherent states under the action of a group by means of square integrable representations. This work shows that admissible vectors can be seen as weights with central support on the (left) group von…
The method of alternating projections (MAP) is a common method for solving feasibility problems. While employed traditionally to subspaces or to convex sets, little was known about the behavior of the MAP in the nonconvex case until 2009,…
Complete eigenstructure, e.g., eigenvalues with multiplicities and minimal indices, of a skew-symmetric matrix pencil may change drastically if the matrix coefficients of the pencil are subjected to (even small) perturbations. These changes…
Exploiting tools from algebraic geometry, the problem of finiteness of determination of accessibility/strong accessibility is investigated for polynomial systems and also for analytic systems that are immersible into polynomial systems. The…
The magnetization curve of a type II superconductor in general is hysteretic even when the vortices exhibit no volume or surface pinning. This geometric irreversibility, caused by an edge barrier for flux penetration, is absent only when…