Related papers: Rank Function Equations and their solution sets

In this paper, we study the rank of matrices of bicomplex numbers. The relationship between rank, idempotent column rank and idempotent row rank is examined. Then, the solution of a system of equations in bicomplex space is presented using…

A presentation of numerical range for rectangular matrices is undertaken in this paper, introducing two different definitions and elaborating basic properties. Then we are extended to the treatment of rank-k numerical range.

We consider the problem of exact low-rank matrix completion from a geometric viewpoint: given a partially filled matrix M, we keep the positions of specified and unspecified entries fixed, and study how the minimal completion rank depends…

We establish certain topological properties of rank understood as a function on the set of invariant measures on a topological dynamical system. To be exact, we show that rank is of Young class LU (i.e., it is the limit of an increasing…

In this paper, we show that the low rank matrix completion problem can be reduced to the problem of finding the rank of a certain tensor.

We study the closure of the projection of the (nonconvex) cone of rank restricted positive semidefinite matrices onto subsets of the matrix entries. This defines the feasible sets for semidefinite completion problems with restrictions on…

For a class of integral operators with kernels metric functions on manifold we find some necessary and sufficient conditions to have finite rank. The problem we pose has a stochastic nature and boils down to the following alternative…

We develop a systematic way to solve linear equations involving tensors of arbitrary rank. We start off with the case of a rank $3$ tensor, which appears in many applications, and after finding the condition for a unique solution we derive…

The paper explores the concept of the rank of a bicomplex matrix, delving into four distinct types of ranks and investigating conditions under which these ranks are equivalent. It also defines and analyzes the concept of idempotent row…

In this note, we give a rank function axiomatization for delta-matroids and study the corresponding rank generating function. We relate an evaluation of the rank generating function to the number of independent sets of the delta-matroid,…

In this paper we study various versions of extension complexity for polygons through the study of factorization ranks of their slack matrices. In particular, we develop a new asymptotic lower bound for their nonnegative rank, shortening the…

Recent work of Qi et al. arXiv:2004.11240v7 proposes a set of axioms for tensor rank functions. The current paper presents examples showing that their axioms allow rank functions to have some undesirable properties, and a stronger set of…

For a rational function of several variables with nonnegative imaginary part on the upper poly-half-plane, the matrix representations are obtained.

We consider conjugation action of symmetric group on the semigroup of all partial functions and develop a machinery to investigate character formulas and multiplicities. In particular, we determine nilpotent matrices whose orbit under…

In this paper we illustrate by some examples the connection between the number of solutions of polynomial equations satisfying degree conditions and the number of rank I matrices related to persymmetric matrices.

We study the problem of enumerating answers of Conjunctive Queries ranked according to a given ranking function. Our main contribution is a novel algorithm with small preprocessing time, logarithmic delay, and non-trivial space usage during…

This preliminary note presents a heuristic for determining rank constrained solutions to linear matrix equations (LME). The method proposed here is based on minimizing a non-convex quadratic functional, which will hence-forth be termed as…

Given a finite and non-empty set $X$ and randomly selected specific functions and relations on $X$, we investigate the existence and non-existence of fixed points and reflexive points, respectively. First, we consider the class of…

Except for a limited number of cases, a complete classification of the Diophantine sets of polynomial rings and fields of rational functions seems out of reach at present. We contribute to this problem by proving that several natural sets…

Differentiable systems in this paper means systems of equations that are described by differentiable real functions in real matrix variables. This paper proposes algorithms for finding minimal rank solutions to such systems over (arbitrary…