Linear Algebra

Linear algebra is one of the most widely used mathematical theories around, and has applications in virtually every area of mathematics, including multivariate calculus, differential equations, and probability theory. The purpose of this book is to bridge the gap between the abstract theoretical aspects and the computational applications of linear algebra. The aim of this book is two-fold: to introduce the fundamental concepts of linear algebra and to apply the theorems in computation-oriented applications. Features: - Covers theory and applications emphasizing topics useful in other disciplines - Presents a brief introduction of some aspects of abstract algebra that relate directly to linear algebra, such as groups, rings, modules, fields and polynomials over fields. The aim of this book is two-fold: to introduce the fundamental concepts of linear algebra and to apply the theorems in computation-oriented applications. The book is suitable for a one semester course in linear algebra that can be used in a variety of contexts. The presentation of the material combines definitions and proofs with an emphasis on computational applications, providing examples that illustrate the use of software packages such as Mathematica®, Maple®, and Sage. Features:- Introduces the fundamental concepts of linear algebra and applies the theorems in computation-oriented applications- Presents a brief introduction of some aspects of abstract algebra that relate directly to linear algebra, such as groups, rings, modules, fields and polynomials over fields.