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OverviewThis is a two-volume set. Both volumes focus on linear algebra for graduate students in mathematics, the sciences, and economics, who have: a prior undergraduate course in the subject; a basic understanding of matrix algebra; and some proficiency with mathematical proofs. Proofs are emphasized and the overall objective is to understand the structure of linear operators as the key to solving problems in which they arise. Both volumes have been used for several years in a one-year course sequence, Linear Algebra I and II, offered at New York University's Courant Institute. The first volume re-examines basic notions of linear algebra: vector spaces, linear operators, duality, determinants, diagonalization, and inner product spaces, giving an overview of linear algebra with sufficient mathematical precision for advanced use of the subject. This book provides a nice and varied selection of exercises; examples are well-crafted and provide a clear understanding of the methods involved. New notions are well motivated and interdisciplinary connections are often provided, to give a more intuitive and complete vision of linear algebra. Computational aspects are fully covered, but the study of linear operators remains the focus of study in this book. The first three chapters of the second volume round out the coverage of traditional linear algebra topics: generalized eigenspaces, further applications of Jordan form, as well as bilinear, quadratic, and multilinear forms. The final two chapters are different, being more or less self-contained accounts of special topics that explore more advanced aspects of modern algebra: tensor fields, manifolds, and vector calculus in Chapter 4 and matrix Lie groups in Chapter 5. The reader can choose to pursue either chapter. Both deal with vast topics in contemporary mathematics. They include historical commentary on how modern views evolved, as well as examples from geometry and the physical sciences in which these topics are important. The second volume provides a nice and varied selection of exercises; examples are well-crafted and provide a clear understanding of the methods involved . Full Product DetailsAuthor: Federick P. Greenleaf , Sophie MarquesPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 1.060kg ISBN: 9781470461607ISBN 10: 1470461609 Pages: 569 Publication Date: 30 September 2020 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsPart : Vector Spaces Over a Field $\mathbb{K}$ Linear Operators $T: V \to W$ Duality and the Dual Space $V^*$ Determinants The Diagonalization Problem Inner Product Spaces Index Part : Generalized Eigenspaces and the Jordon Decomposition Further Applications of Jordon Form Bilinear, Quadratic, and Multilinear Forms Tensor Fields, Manifolds, and Vector Calculus Matrix Lie Groups Bibliography.ReviewsAuthor InformationFrederick P. Greenleaf, Courant Institute, New York University, NY, USA. Sophie Marques, Stellenbosch University, South Africa. Tab Content 6Author Website:Countries AvailableAll regions |
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