Related papers: Disjoint weighing matrices
We review a class of matrix models whose degrees of freedom are matrices with anticommuting elements. We discuss the properties of the adjoint fermion one-, two- and gauge invariant D-dimensional matrix models at large-N and compare them…
Pairwise comparison matrices are frequently applied in multi-criteria decision making. A weight vector is called efficient if no other weight vector is at least as good in approximating the elements of the pairwise comparison matrix, and…
To apportion a complex matrix means to apply a similarity so that all entries of the resulting matrix have the same magnitude. We initiate the study of apportionment, both by unitary matrix similarity and general matrix similarity. There…
Many natural, technological, and social systems incorporate multiway interactions, yet are characterized and measured on the basis of weighted pairwise interactions. In this article, I propose a family of models in which pairwise…
Conjugation covariants of matrices are applied to study the real algebraic variety consisting of complex Hermitian matrices with a bounded number of distinct eigenvalues. A minimal generating system of the vanishing ideal of degenerate…
We consider some special type extensions of an arbitrary Lie algebra, which we call universal extensions. We show that these extensions are in one-to-one correspondence with finite dimensional associative commutative algebras. We also…
We present a general class of machine learning algorithms called parametric matrix models. In contrast with most existing machine learning models that imitate the biology of neurons, parametric matrix models use matrix equations that…
This paper begins the exploration of what we call measures of association between two irreducible complex projective varieties of the same dimension. The idea is to study from various points of view the minimal complexity of correspondences…
The double-direction orthogonalization algorithm is applied to construct sequences of polynomials, which are orthogonal over the interval [0,1]with the weighting function 1. Functional and recurrent relations are derived for the sequences…
Variational and divergence symmetries are studied in this paper for the whole class of linear and nonlinear equations of maximal symmetry, and the associated first integrals are given in explicit form. All the main results obtained are…
We introduce weighted cycles on weaves of general Dynkin types and define a skew-symmetrizable intersection pairing between weighted cycles. We prove that weighted cycles on a weave form a Laurent polynomial algebra and construct a…
A mixed lattice is a lattice-type structure consisting of a set with two partial orderings, and generalizing the notion of a lattice. Mixed lattice theory has previously been studied in various algebraic structures, such as groups and…
Given a bivariate weight function defined on the positive quadrant of $\mathbb{R}^2$, we study polynomials in two variables orthogonal with respect to varying measures obtained by special modifications of this weight function. In…
Matrices are the most common representations of graphs. They are also used for the representation of algebras and cluster algebras. This paper shows some properties of matrices in order to facilitate the understanding and locating…
Orthogonal arrays play a fundamental role in many applications. However, constructing orthogonal arrays with the required parameters for an application usually is extremely difficult and, sometimes, even impossible. Hence there is an…
This survey presents a necessarily incomplete (and biased) overview of results at the intersection of arithmetic circuit complexity, structured matrices and deep learning. Recently there has been some research activity in replacing…
A result on the structure of expansive matrices in an indefinite inner product space is derived, which exhibits the largest unitary compression of the matrix.
The question "What is category theory" is approached by focusing on universal mapping properties and adjoint functors. Category theory organizes mathematics using morphisms that transmit structure and determination. Structures of…
In this paper we outline a Matrix Ansatz approach to some problems of combinatorial enumeration. The idea is that many interesting quantities can be expressed in terms of products of matrices, where the matrices obey certain relations. We…
We define the concept of weighted lattice polynomial functions as lattice polynomial functions constructed from both variables and parameters. We provide equivalent forms of these functions in an arbitrary bounded distributive lattice. We…