Related papers: Smith Normal Forms of Incidence Matrices
Interference effects are an important consequence of a correct description in physics theories within and beyond the Standard Model (SM) of particle physics. However, many current theoretical descriptions as well as experimental searches…
Explicit formulae are given for the nine possible induced matrix norms corresponding to the 1-, 2-, and $\infty$-norms for Euclidean space. The complexity of computing these norms is investigated.
A novel factorization for the sum of two single-pair matrices is established as product of lower-triangular, tridiagonal, and upper-triangular matrices, leading to semi-closed-form formulas for tridiagonal matrix inversion. Subsequent…
In these notes we review recent progress (and, in Section \ref{sec:ados}, we announce a new result) concerning the statistical properties of the spectrum of Wigner random matrices.
We define {\em incidence matrices} to be zero-one matrices with no zero rows or columns. A classification of incidence matrices is considered for which conditions of symmetry by transposition, having no repeated rows/columns, or…
We propose a way to study one-dimensional statistical mechanics models with complex-valued action using transfer operators. The argument consists of two steps. First, the contour of integration is deformed so that the associated transfer…
This paper is devoted to a discussion of specific properties of invariants in the theory of forms.
Schemes for exact multiplication of small matrices have a large symmetry group. This group defines an equivalence relation on the set of multiplication schemes. There are algorithms to decide whether two schemes are equivalent. However, for…
This article presents an overview of the theory of integrable systems with symmetries, focusing on toric systems, semitoric systems, and their classifications via decorated polygons. We discuss certain one-parameter families of integrable…
In this talk we go over several new developments regarding the techniques for a large class of non-hermitian matrix models with unitary randomness (complex random numbers). In particular, we discuss: (a) - A diagrammatic approach based on a…
The Nystr\"om method is a popular choice for finding a low-rank approximation to a symmetric positive semi-definite matrix. The method can fail when applied to symmetric indefinite matrices, for which the error can be unboundedly large. In…
We present an alternative account of the problem of classifying and finding normal forms for arbitrary bilinear forms. Beginning from basic results developed by Riehm, our solution to this problem hinges on the classification of…
The recent wide recognition of the existence of neutrino oscillations concludes the pioneer stage of these studies and poses the problem of how to communicate effectively the basic aspects of this branch of science. In fact, the phenomenon…
In what follows we give a quick tour through the field of minimal submanifolds, starting at the definition and the classical results and ending up with current areas of research.
The intended purpose of this work is to provide the reader with a comprehensive, state-of-the art presentation of the theory of complex Hadamard matrices, or at least report on the very recent advances. This manuscript consists of three…
We give an informal introduction to model categories, and treat three important examples in some details: the category of small categories, the category of dg algebras, and the category of small dg categories.
Machine learning presents a general, systematic framework for the generation of formal theoretical models for physical description and prediction. Tentatively standard linear modeling techniques are reviewed; followed by a brief discussion…
Grating spectra exhibit sharp variations of the scattered light, known as grating anomalies. The latter are due to resonances that have fascinated specialists of optics and physics for decades and are nowadays used in many applications. We…
These informal notes deal with some basic properties of metric spaces, especially concerning lengths of curves.
Associated to each complex-valued random variable satisfying appropriate integrability conditions, we introduce a different generalization of the Stirling numbers of the second kind. Various equivalent definitions are provided. Attention,…