Linear Algebra: An Introduction

Synopsis

In this appealing and well-written text, Richard Bronson gives readers a substructure for a firm understanding of the abstract concepts of linear algebra and its applications. The author starts with the concrete and computational (a 3 x 5 matrix describing a stores inventory) and leads the reader to a choice of major applications (Markov chains, least squares approximation, and solution of differential equations using Jordan normal form). The first three chapters address the basics: matrices, vector spaces, and linear transformations. The next three cover eigen values, Euclidean inner products, and Jordan canonical forms, offering possibilities that can be tailored to the instructors taste and to the length of the course. Bronsons approach to computation is modern and algorithmic, and his theory is clean and straightforward. Throughout, the views of the theory presented are broad and balanced. Key material is highlighted in the text and summarized at end of each chapter. The book also includes ample exercises with answers and hints. With its inclusion of all the needed pedagogical features, this text will be a pleasure for teachers and students alike. It: gives a firm substructure for understanding linear algebra and its applications; introduces deductive reasoning and helps the reader develop a facility with mathematical proofs; begins with the concrete and computational (a 3 x 5 matrix describing a stores inventory) and leads the reader to a choice of major applications (Markov chains, least squares approximation, and solution of differential equations using Jordan normal form); covers matrices, vector spaces, linear transformations, as well as applications to Jordan canonical forms, differential equations, and Markov chains; gives computational algorithms for finding eigen values and eigen vectors; provides a balanced approach to computation and theory; highlights key material in the text as well as in summaries at the end of each chapter; and includes ample exercises with answers and hints, in addition to other learning features.