相关论文: Convenient parameterizations of matrices in terms …
We determine the most general group of equivalence transformations for a family of differential equations defined by an arbitrary vector field on a manifold. We also find all invariants and differential invariants for this group up to the…
In this work we classify the at-point regularities of set-valued mappings into two categories and then we analyze their relationship through several implications and examples. After this theoretical tour, we use the subregularity properties…
In this dissertation, we explore the structure of inversion graphs of permutations--a class of graphs that naturally arises by representing each permutation as a graph, where vertices correspond to entries and edges encode inversions.…
The purpose of this text is to provide an accessible introduction to a set of recently developed algorithms for factorizing matrices. These new algorithms attain high practical speed by reducing the dimensionality of intermediate…
It is known that some cosmological perturbations are conformal invariant. This facilitates the studies of perturbations within some gravitational theories alternative to general relativity, for example the scalar-tensor theory, because it…
Matrices are typically considered over fields or rings. Motivated by applications in parametric differential equations and data-driven modeling, we suggest to study matrices with entries from a Hilbert space and present an elementary theory…
In recent years, random matrices have come to play a major role in computational mathematics, but most of the classical areas of random matrix theory remain the province of experts. Over the last decade, with the advent of matrix…
We present further properties of a previously proposed recursive scheme for parameterisation of n-by-n unitary matrices. We show that the factors in the recursive formula may be introduced in any desired order. The method is used to study…
In this note, we define a Gaussian probability distribution over matrices. We prove some useful properties of this distribution, namely, the fact that marginalization, conditioning, and affine transformations preserve the matrix Gaussian…
The sample covariance matrix becomes non-invertible in high-dimensional settings, making classical multivariate statistical methods inapplicable. Various regularization techniques address this issue by imposing a structured target matrix to…
Eigenvectors of large matrices (and graphs) play an essential role in combinatorics and theoretical computer science. The goal of this survey is to provide an up-to-date account on properties of eigenvectors when the matrix (or graph) is…
Equiangular Algorithm generates a set of equiangular normalized vectors with given angle {\theta} using a set of linearly independence vectors in a real inner product space, which span the same subspaces. The outcome of EA on column vectors…
We introduce meta-factorization, a theory that describes matrix decompositions as solutions of linear matrix equations: the projector and the reconstruction equation. Meta-factorization reconstructs known factorizations, reveals their…
There is growing body of learning problems for which it is natural to organize the parameters into matrix, so as to appropriately regularize the parameters under some matrix norm (in order to impose some more sophisticated prior knowledge).…
In the previous article we introduced the new concept of mixed representations of quivers and described the generators of their algebras of invariants. In this article we describe the defining relations of these algebras. Some applications…
A generalized definition of the determinant of matrices is given, which is compatible with the usual determinant for square matrices and keeps many important properties, such as being an alternating multilinear function, keeping…
We present a matrix-based algorithm for deciding if the parametrization of a curve or a surface is invertible or not, and for computing the inverse of the parametrization if it exists.
A unified approach to parametrization of the mixing matrix for $N$ generations is developed. This approach not only has a clear geometrical underpinning but also has the advantage of being economical and recursive and leads in a natural way…
This short course offers a new perspective on randomized algorithms for matrix computations. It explores the distinct ways in which probability can be used to design algorithms for numerical linear algebra. Each design template is…
The multiplicative and additive compounds of a matrix play an important role in several fields of mathematics including geometry, multi-linear algebra, combinatorics, and the analysis of nonlinear time-varying dynamical systems. There is a…