Applied Linear Algebra and Matrix Analysis

This new book offers a fresh approach to matrix and linear algebra by providinga balanced blend of applications theory and computation while highlightingtheir i... » 

This new book offers a fresh approach to matrix and linear algebra by providinga balanced blend of applications theory and computation while highlightingtheir interdependence. Intended for a onesemester course Applied LinearAlgebra and Matrix Analysis places special emphasis on linear algebra as anexperimental science with numerous examples computer exercises and projects.While the flavor is heavily computational and experimental the text isindependent of specific hardware or software platforms. Throughout the booksignificant motivating examples are woven into the text and each section endswith a set of exercises. The student will develop a solid foundation in thefollowing topics Gaussian elimination and other operations with matricesbasic properties of matrix and determinant algebra standard Euclidean spacesboth real and complex geometrical aspects of vectors such as norm dotproduct and angle eigenvalues eigenvectors and discrete dynamical systemsgeneral norm and innerproduct concepts for abstract vector spaces For manystudents the tools of matrix and linear algebra will be as fundamental intheir professional work as the tools of calculus thus it is important toensure that students appreciate the utility and beauty of these subjects aswell as the mechanics. By including applied mathematics and mathematicalmodeling this new textbook will teach students how concepts of matrix andlinear algebra make concrete problems workable. Thomas S. Shores is Professorof Mathematics at the University of Nebraska Lincoln where he has receivedawards for his teaching. His research touches on group theory commutativealgebra mathematical modeling numerical analysis and inverse theory. TOCPreface. Linear Systems of Equations. Matrix Algebra. Vector Spaces.Geometrical Aspects of Standard Spaces. The Eigenvalue Problem. GeometricalAspects of Abstract Spaces. Table of Symbols. Answers to Selected Exercises.References. Index. «