Related papers: Generalization of real interval matrices to other …
Our aim in this paper is to initiate the study of exponent semigroups for rational matrices. We prove that every numerical semigroup is the exponent semigroup of some rational matrix. We also obtain lower bounds on the size of such matrices…
Let $n$ and $p$ be non-negative integers with $n \geq p$, and $S$ be a linear subspace of the space of all $n$ by $p$ matrices with entries in a field $\mathbb{K}$. A classical theorem of Flanders states that $S$ contains a matrix with rank…
A real $n$-by-$n$ idempotent matrix $A$ with all entries having the same absolute value is called {\it absolutely flat}. We consider the possible ranks of such matrices and herein characterize the triples: size, constant, and rank for which…
The nonnegative integer rank of a matrix is a variant of the classical nonnegative rank, introduced in the 1980s, where factorizations are required to have integer entries. While computing nonnegative integer rank is generally very hard, we…
Accurate estimation of camera matrices is an important step in structure from motion algorithms. In this paper we introduce a novel rank constraint on collections of fundamental matrices in multi-view settings. We show that in general, with…
The cospark of a matrix is the cardinality of the sparsest vector in the column space of the matrix. Computing the cospark of a matrix is well known to be an NP hard problem. Given the sparsity pattern (i.e., the locations of the non-zero…
Motivated by recent works on statistics of matrices over sets of number theoretic interest, we study matrices with entries from arbitrary finite subsets $\mathcal A$ of finite rank multiplicative groups infields of characteristic zero. We…
Random matrix theory is a well-developed area of probability theory that has numerous connections with other areas of mathematics and its applications. Much of the literature in this area is concerned with matrices that possess many exact…
Recently, it was shown that most popular IR measures are not interval-scaled, implying that decades of experimental IR research used potentially improper methods, which may have produced questionable results. However, it was unclear if and…
We investigate the problem of completing partial matrices to rank-one matrices in the standard simplex. The motivation for studying this problem comes from statistics: A lack of eligible completion can provide a falsification test for…
Every sufficiently big matrix with small spectral norm has a nearby low-rank matrix if the distance is measured in the maximum norm (Udell & Townsend, SIAM J Math Data Sci, 2019). We use the Hanson--Wright inequality to improve the estimate…
A complete theory of the relationship between the minimal bases and indices of rational matrices and those of their strong linearizations is presented. Such theory is based on establishing first the relationships between the minimal bases…
Matrix regression plays an important role in modern data analysis due to its ability to handle complex relationships involving both matrix and vector variables. We propose a class of regularized regression models capable of predicting both…
A real symmetric matrix $M$ is completely positive semidefinite if it admits a Gram representation by (Hermitian) positive semidefinite matrices of any size $d$. The smallest such $d$ is called the (complex) completely positive semidefinite…
The iterative method of Sinkhorn allows, starting from an arbitrary real matrix with non-negative entries, to find a so-called 'scaled matrix' which is doubly stochastic, i.e. a matrix with all entries in the interval (0, 1) and with all…
Linear algebra's main concerns are sets of vectors, linear functions, subspaces, linear systems, matrices and concepts about those, such as whether the solution of linear system exists or is unique; a set of vectors is linearly independent…
To reliably model real robot characteristics, interval linear systems of equations allow to describe families of problems that consider sets of values. This allows to easily account for typical complexities such as sets of joint states and…
We determine the rank of a random matrix over an arbitrary field with prescribed numbers of non-zero entries in each row and column. As an application we obtain a formula for the rate of low-density parity check codes. This formula…
Structured matrices with symbolic sizes appear frequently in the literature, especially in the description of algorithms for linear algebra. Recent work has treated these symbolic structured matrices themselves as computational objects,…
A nonnegative matrix A is said to be strongly robust if its max-algebraic eigencone is universally reachable, i.e., if the orbit of any initial vector ends up with a max-algebraic eigenvector of A. Consider the case when the initial vector…