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This paper considers compressed sensing matrices and neighborliness of a centrally symmetric convex polytope generated by vectors $\pm X_1,...,\pm X_N\in\R^n$, ($N\ge n$). We introduce a class of random sampling matrices and show that they…

Probability · Mathematics 2009-05-01 Radosław Adamczak , Alexander E. Litvak , Alain Pajor , Nicole Tomczak-Jaegermann

We prove matching direct and inverse theorems for (algebraic) polynomial approximation with doubling weights $w$ having finitely many zeros and singularities (i.e., points where $w$ becomes infinite) on an interval and not too ``rapidly…

Classical Analysis and ODEs · Mathematics 2015-07-20 Kirill A. Kopotun

We characterize some variations of pseudoskeleton (also called CUR) decompositions for matrices and tensors over arbitrary fields. These characterizations extend previous results to arbitrary fields and to decompositions which use…

Numerical Analysis · Mathematics 2022-07-01 Keaton Hamm

The purpose of this note is to give explicit criteria to determine whether a real generalized Cartan matrix is of finite type, affine type or of hyperbolic type by considering the principal minors and the inverse of the matrix. In…

Representation Theory · Mathematics 2007-05-23 Hechun Zhang

We generalize the Wedderburn rank reduction formula by replacing the inverse with the Moore--Penrose pseudoinverse. In particular, this allows one to remove the non--singularity of a certain matrix from assumptions. The results implies in a…

Numerical Analysis · Mathematics 2024-06-07 Oskar Kędzierski

While an explicit basis is common in the study of Euclidean spaces, it is usually implied in the study of inertial relativistic systems. There are some conceptual advantages to including the basis in the study of special relativistic…

Classical Physics · Physics 2011-04-27 Peeter Joot

The notion of a Moore-Penrose inverse (M-P inverse) was introduced by Moore in 1920 and rediscovered by Penrose in 1955. The M-P inverse of a complex matrix is a special type of inverse which is unique, always exists, and can be computed…

Logic in Computer Science · Computer Science 2023-09-01 Robin Cockett , Jean-Simon Pacaud Lemay

We consider the inverse problem of finding a magnitude-symmetric matrix (matrix with opposing off-diagonal entries equal in magnitude) with a prescribed set of principal minors. This problem is closely related to the theory of recognizing…

Combinatorics · Mathematics 2024-09-09 Victor-Emmanuel Brunel , John Urschel

We introduce the notion of one-sided mapping cones of positive linear maps between matrix algebras. These are convex cones of maps that are invariant under compositions by completely positive maps from either the left or right side. The…

Operator Algebras · Mathematics 2022-11-17 Mark Girard , Seung-Hyeok Kye , Erling Størmer

In this paper it is shown that a generalized circulant matrix underlies every weakly Coupled Map Lattice (CML), independently of the form of the coupling term. Therefore, this matrix will appear always perturbative methods are used to get…

Pattern Formation and Solitons · Physics 2009-03-25 M. Dolores Sotelo Herrera Jesus San Martin

The objective of this paper is, in the main, twofold: Firstly, to develop an algebraic setting for dealing with Bell polynomials and related extensions. Secondly, based on the author's previous work on multivariate Stirling polynomials…

Combinatorics · Mathematics 2021-01-28 Alfred Schreiber

We derive weighted summation identities involving the second order recurrence sequence $\{w_n\} =\{ w_n(a,b; p, q)\}$ defined by $w_0 = a,\,w_1 = b;\,w_n = pw_{n - 1} - qw_{n - 2}\, (n \ge 2)$, where $a$, $b$, $p$ and $q$ are arbitrary…

Number Theory · Mathematics 2018-04-13 Kunle Adegoke

Power nonnegative matrices are defined as complex matrices having at least one nonnegative integer power. We exploit the possibility of deriving a Perron Frobenius-like theory for these matrices, obtaining three main results and drawing…

Numerical Analysis · Mathematics 2013-11-21 F. Tudisco , V. Cardinali , C. Di Fiore

We study open-closed discrete mappings that satisfy the weighted estimate of the distortion of modulus of families of paths. It is proved that the mappings mentioned above have a continuous extension into the isolated point of the boundary,…

Complex Variables · Mathematics 2020-04-30 Evgeny Sevost'yanov

The M-P (Moore-Penrose) pseudoinverse has as a key application the computation of least-squares solutions of inconsistent systems of linear equations. Irrespective of whether a given input matrix is sparse, its M-P pseudoinverse can be…

Optimization and Control · Mathematics 2020-11-06 Marcia Fampa , Jon Lee , Gabriel Ponte

In this paper we consider the generalized inverse iteration for computing ground states of the Gross-Pitaevskii eigenvector problem (GPE). For that we prove explicit linear convergence rates that depend on the maximum eigenvalue in…

Numerical Analysis · Mathematics 2024-03-11 Patrick Henning

Bernstein polynomials, long a staple of approximation theory and computational geometry, have also increasingly become of interest in finite element methods. Many fundamental problems in interpolation and approximation give rise to…

Numerical Analysis · Mathematics 2019-07-15 Larray Allen , Robert C. Kirby

This paper examines the potential role of unit consistency as a system design principle. Unit-consistent generalized matrix inverses and unit-invariant matrix decompositions are derived in support of this principle. Applications of the…

Numerical Analysis · Computer Science 2017-07-12 Jeffrey Uhlmann

This paper examines the properties of real symmetric square matrices with a constant value for the main diagonal elements and another constant value for all off-diagonal elements. This matrix form is a simple subclass of circulant matrices,…

Statistics Theory · Mathematics 2021-09-14 Ben O'Neill

This work investigates preserving and reversing unimodality and convexity properties for sequences under transformations defined by sign-regular kernels. It is shown that these transformations only preserve these properties if the kernels…

Classical Analysis and ODEs · Mathematics 2025-02-20 Zakaria Derbazi