Linear Algebra and Its Applications

From Tzuong-Tsieng Moh, a seasoned expert in algebra, comes a new book for students to better understand linear algebra. Writing from an experienced standpoint, Moh covers the many standard aspects comprising linear algebra, such as echelon forms, matrix algebra, linear transformations, and more. Moh further includes several advanced topics and applications, as well as self-correcting codes, Heisenberg's uncertainty principle, Maxwell's equations in relativity form, Google's search engine, and the theory of finitely generated modules over a PID. This book is ideal for both newcomers and experienced readers who want to attain a deeper understanding on both the basics and advanced topics of linear algebra and its vast applications. The wide range of topics combined with the depth of each discussion make it essential to be on the shelf of every mathematical beginner and enthusiast.Contents: PrefacePreliminariesModuleDeterminants and Multilinear AlgebrasInner Product SpacesBilinear Forms and DecompositionsComputational Linear AlgebraIndex
Readership: Graduate students and researchers interested in the basic and advanced topics of linear algebra and its applications. Cauchy–Binet Formula;Jordan Canonical Form;Least Squares Approximations;Matrix Algebra;Perron–Frobenius Theorem;Smith Normal Form;Sylvester's Law of Inertia0Key Features:The author, Tzuong-Tsieng Moh, is an expert in the field of algebraThe book covers a wide range of topics while delving into deep discussion about each of them. The subject can be classified into theory, application and numerical computation and the book covers all these aspectsThe book includes beginner and advanced topics. There are finite dimension vector spaces which are foundation of the theory of matrices and determinants. There are also infinite dimension vector spaces which are illustrated by inner product spaces and Hilbert space