Linear algebra

Includes bibliographical references and index.

Linear Algebra offers a unified treatment of both matrix-oriented and theoretical approaches to the course, which will be useful for classes with a mix of mathematics, physics, engineering, and computer science students. Major topics include singular value decomposition, the spectral theorem, linear systems of equations, vector spaces, linear maps, matrices, eigenvalues and eigenvectors, linear independence, bases, coordinates, dimension, matrix factorizations, inner products, norms, and determinants. Introduces central topics, such as vector spaces, linear maps, linear dependence and eigenvalues early in the book with the aim of helping students transition from calculus to rigorous mathematics. Motivates the reader whilst introducing new topics, definitions, and appropriate examples in connection with the core concepts presented early in the text so that students will be able to go back to these vital notions and, by the time the course ends, will have worked with them extensively. Includes many pedagogical features, such as: 'Quick Exercises' throughout with answers upside-down at the bottom of the page; periodic 'Perspectives' that collect various viewpoints on particular topics developed throughout the text; and numerous in-text examples, end-of-chapter exercises, and hints and answers to selected problems at the end of the book.