Related papers: Vector Space and Matrix Methods in Signal and Syst…
In our article we consider some algebraical methods which may be useful in some inverse spectral problems. The reconstraction of the matrix from its minors is considered.
In the decade since 2010, successes in artificial intelligence have been at the forefront of computer science and technology, and vector space models have solidified a position at the forefront of artificial intelligence. At the same time,…
This is the first of two papers on partition functions and the index theory of transversally elliptic operators. In this paper we only discuss algebraic and combinatorial issues related to partition functions. The applications to index…
Data are often represented as graphs. Many common tasks in data science are based on distances between entities. While some data science methodologies natively take graphs as their input, there are many more that take their input in…
Tensors are ubiquitous in statistics and data analysis. The central object that links data science to tensor theory and algebra is that of a model with latent variables. We provide an overview of tensor theory, with a particular emphasis on…
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…
Linear systems are the bedrock of virtually all numerical computation. Machine learning poses specific challenges for the solution of such systems due to their scale, characteristic structure, stochasticity and the central role of…
Large amount of multidimensional data represented by multiway arrays or tensors are prevalent in modern applications across various fields such as chemometrics, genomics, physics, psychology, and signal processing. The structural complexity…
Given two sets of basis vectors in n-dimensional space, there exists a relation between their lengths and mutual angles, expressed as relations between the two metric matrices and the mixed matrix. In this paper these relations are given,…
Observations which are realizations from some continuous process are frequent in sciences, engineering, economics, and other fields. We consider linear models, with possible random effects, where the responses are random functions in a…
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
This book is a continuation of the book n-linear algebra of type I and its applications. Most of the properties that could not be derived or defined for n-linear algebra of type I is made possible in this new structure: n-linear algebra of…
We review the recent programme of using machine-learning to explore the landscape of mathematical problems. With this paradigm as a model for human intuition - complementary to and in contrast with the more formalistic approach of automated…
En esta serie de tres articulos, damos una exposicion de varios resultados y problemas abiertos en tres areas de la combinatoria algebraica y geometrica: las matrices totalmente no negativas, las representaciones del grupo simetrico, y los…
In the last quarter of a century, algebraic statistics has established itself as an expanding field which uses multilinear algebra, commutative algebra, computational algebra, geometry, and combinatorics to tackle problems in mathematical…
In engineering practice one often encounters planar problems, where the corresponding vector space of forces, velocities or (infinitesimal) displacements is three dimensional. This paper shows how these spaces can be factorized, such that…
We consider the vector space of $n \times n$ matrices over $\mathbb C$, Fermi operators and operators constructed from these matrices and Fermi operators. The properties of these operators are studied with respect to the underlying…
Rigorous modelling of natural and industrial systems still conveys various challenges related to abstractions, methods to proceed with and easy-to-use tools to build, compose and reason on models. Operads are mathematical structures that…
Much recent work has addressed the solution of a family of partial differential equations by computing the inverse operator map between the input and solution space. Toward this end, we incorporate function-valued reproducing kernel Hilbert…
The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The…