Hot Topics in Linear Algebra


Series: Mathematics Research Developments
BISAC: MAT002050

Linear 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 generalized 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 modeling 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 generalized 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 modeling 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.
(Imprint: Nova)

Table of Contents

Table of Contents


Chapter 1. Computing Generalized Inverses Using Gradient-Based Dynamical Systems
(Predrag S. Stanimirović and Yimin Wei, University of Niš, Faculty of Sciences and Mathematics,
Niš, Serbia, and others)

Chapter 2. Cramer’s Rules for Sylvester-Type Matrix Equations
(Ivan I. Kyrchei, Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, NAS of Ukraine, Lviv, Ukraine)

Chapter 3. BICR Algorithm for Computing Generalized Bisymmetric Solutions of General Coupled Matrix Equations
(Masoud Hajarian, Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, General Campus, Evin, Tehran, Iran)

Chapter 4. System of Mixed Generalized Sylvester-Type Quaternion Matrix Equations
(Abdur Rehman, Ivan I. Kyrcheiy, Muhammad Akram, Ilyas Ali and Abdul Shakoor, University of Engineering and Technology, Lahore, Punjab, Pakistan, and others)

Chapter 5. Hessenberg Matrices: Properties and Some Applications
(Taras Goy and Roman Zatorsky, Vasyl Stefanyk Precarpathian National University, Ivano-Frankivsk, Ukraine)

Chapter 6. Equivalence of Polynomial Matrices over a Field
(Volodymyr M. Prokip, Department of Algebra, Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, NAS of Ukraine, Lviv, Ukraine)

Chapter 7. Matrices in Chemical Problems Modeled Using Directed Graphs and Multigraphs
(Victor Martinez-Luaces, Electrochemistry Multidisciplinary Research Group, Faculty of Engineering, UdelaR, Montevideo, Uruguay)

Chapter 8. Engaging Students in the Learning of Linear Algebra
(Marta G. Caligaris, Georgina B. Rodríguez and Lorena F. Laugero, Grupo Ingeniería and Educación, Universidad Tecnológica Nacional, San Nicolás, Buenos Aires, Argentina)


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