Related papers: Some applications of linear algebraic methods in c…

I construct a Lanczos process on a large and sparse matrix and use the results of this iteration to compute the inverse square root of the same matrix. The algorithm is a stable version of an earlier proposal by the author. It can be used…

We consider a hierarchy of many particle systems on the line with polynomial potentials separable in parabolic coordinates. Using the Lax representation, written in terms of $2\times 2$ matrices for the whole hierarchy, we construct the…

I present here a pedagogical introduction to the works by Rashel Tublin and Yan V. Fyodorov on random linear systems with quadratic constraints, using tools from Random Matrix Theory and replicas. These notes illustrate and complement the…

Consider a formally self-adjoint first order linear differential operator acting on pairs (2-columns) of complex-valued scalar fields over a 4-manifold without boundary. We examine the geometric content of such an operator and show that it…

We present a practical Newton-based method for computing left eigenvalues of quaternion matrices. It uses only standard real/complex linear-algebra kernels via embeddings and applies to matrices of any size. Extensive tests on literature…

We exhibit an explicit formula for the cardinality of solutions to a class of quadratic matrix equations over finite fields. We prove that the orbits of these solutions under the natural conjugation action of the general linear groups can…

A paper by Cavenagh and Wanless diagnosed the possible intersection of any two transversals of the back circulant Latin square B_n, and used the result to completely determine the spectrum for 2-way k-homogeneous latin trades. We give a…

Semi-Latin squares have been extensively studied. They can be interpreted as a special case of latinized block designs where the number of columns is equal to the number of replicates in the design. Latinized row-column designs are…

We study a class of complex polynomial equations on a finite graph with a view to understanding how holistic phenomena emerge from combinatorial structure. Particular solutions arise from orthogonal projections of regular polytopes,…

Interested in formalizing the generation of fast running code for linear algebra applications, the authors show how an index-free, calculational approach to matrix algebra can be developed by regarding matrices as morphisms of a category…

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…

We give an algorithm for constructing the algebraic hull of a given matrix Lie algebra in characteristic zero. It is based on an algorithm for finding integral linear dependencies of the roots of a polynomial, that is probably of…

Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time…

Partially commutative monoids provide a powerful tool to study graphs, viewingwalks as words whose letters, the edges of the graph, obey a specific commutation rule. A particularclass of traces emerges from this framework, the hikes, whose…

We give some experimental observations on the growth of the norm of certain matrices related to the Mertens function. The results obtained in these experiments convince us that linear algebra may help in the study of Mertens function and…

We show herein that a pattern based on FGLM techniques can be used for computing Gr\"obner bases, or related structures, associated to linear codes. This Gr\"obner bases setting turns out to be strongly related to the combinatorics of the…

We describe a general algorithm for generating various families of ribbon tableaux and computing their spin polynomials. This algorithm is derived from a new matricial coding. An advantage of this new notation lies in the fact that it…

Censor-Hillel et al. [PODC'15] recently showed how to efficiently implement centralized algebraic algorithms for matrix multiplication in the congested clique model, a model of distributed computing that has received increasing attention in…

Partitioning large matrices is an important problem in distributed linear algebra computing (used in ML among others). Briefly, our goal is to perform a sequence of matrix algebra operations in a distributed manner (whenever possible) on…

Potential algebras can be used effectively in the analysis of the quantum systems. In the article, we focus on the systems described by a separable, 2x2 matrix Hamiltonian of the first order in derivatives. We find integrals of motion of…