Description
Book SynopsisLinear algebra is the branch of mathematics concerning vector spaces and linear mappings between such spaces. Systems of linear equations with several unknowns are naturally represented using the formalism of matrices and vectors. So we arrive at the matrix algebra, etc. Linear algebra is central to almost all areas of mathematics. Many ideas and methods of linear algebra were generalised to abstract algebra. Functional analysis studies the infinite-dimensional version of the theory of vector spaces. Combined with calculus, linear algebra facilitates the solution of linear systems of differential equations. Linear algebra is also used in most sciences and engineering areas because it allows for the modelling of many natural phenomena, and efficiently computes with such models. ''Hot Topics in Linear Algebra'' presents original studies in some areas of the leading edge of linear algebra. Each article has been carefully selected in an attempt to present substantial research results across a broad spectrum. Topics discussed herein include recent advances in analysis of various dynamical systems based on the Gradient Neural Network; Cramer's rules for quaternion generalized Sylvester-type matrix equations by using noncommutative row-column determinants; matrix algorithms for finding the generalized bisymmetric solution pair of general coupled Sylvester-type matrix equations; explicit solution formulas of some systems of mixed generalised Sylvester-type quaternion matrix equations; new approaches to studying the properties of Hessenberg matrices by using triangular tables and their functions; researching of polynomial matrices over a field with respect to semi-scalar equivalence; mathematical modelling problems in chemistry with applying mixing problems, which the associated MP-matrices; and some visual apps, designed in Scilab, for the learning of different topics of linear algebra.
Table of ContentsPreface; Computing Generalized Inverses Using Gradient-Based Dynamical Systems; Cramers Rules for Sylvester-Type Matrix Equations; BICR Algorithm for Computing Generalized Bisymmetric Solutions of General Coupled Matrix Equations; System of Mixed Generalized Sylvester-Type Quaternion Matrix Equations; Hessenberg Matrices: Their Properties and Some Applications; Equivalence of Polynomial Matrices over a Field; Matrices in Chemical Problems Modeled Using Directed Graphs and Multigraphs; Engaging Students in the Learning of Linear Algebra; Index.
