Linear Algebra: Algorithms, Applications, and Techniques

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9780123914200: Linear Algebra: Algorithms, Applications, and Techniques

In this appealing and well-written text, Richard Bronson starts with the concrete and computational, and leads the reader to a choice of major applications. The first three chapters address the basics: matrices, vector spaces, and linear transformations. The next three cover eigenvalues, Euclidean inner products, and Jordan canonical forms, offering possibilities that can be tailored to the instructor's taste and to the length of the course. Bronson's 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 and key material is highlighted in the text and summarized at the end of each chapter. The book also includes ample exercises with answers and hints. It introduces deductive reasoning and helps the reader develop a facility with mathematical proofs. It provides a balanced approach to computation and theory by offering computational algorithms for finding eigenvalues and eigenvectors. It offers excellent exercise sets, ranging from drill to theoretical/challeging along with useful and interesting applications not found in other introductory linear algebra texts.

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"The quality of the exercises is better than that of Anton. Bronson's exercises seem more original and less trivial. While he does have routine drill problems his non-routine problems require the student to either extend the student's knowledge base or fill in a portion of a proof."--Renee Britt, Louisiana State University "I appreciate the slow increase in the progression of difficulty with proofs... I regard the exposition as superior. Prof. Bronson's text is the best example I've ever seen of motivating definitions in linear algebra, right from the very first page... Bronson incorporates the application first, thus motivating the definition, going from concrete to abstract, instead of the reverse." --Michael Ecker, The Pennsylvania State University

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