Linear Algebra (Volumes I and II): The Set

This two-volume set is a comprehensive introduction to linear algebra for graduate students in mathematics, sciences, and economics. It covers basic notions, matrix algebra, and computational aspects, with an emphasis on proofs and the structure of linear operators. The first volume re-examines vector spaces, linear operators, and diagonalization, while the second volume covers generalized eigenspaces, Jordan form, bilinear, quadratic, and multilinear forms, as well as special topics such as tensor fields, manifolds, and vector calculus. The books include historical commentary and examples from geometry and the physical sciences.

Format: Paperback / softback
Length: 569 pages
Publication date: 30 September 2020
Publisher: American Mathematical Society

This two-volume set is a comprehensive resource for graduate students in mathematics, the sciences, and economics who have a prior undergraduate course in linear algebra, a basic understanding of matrix algebra, and some proficiency with mathematical proofs. The books focus on linear algebra, emphasizing proofs and the structure of linear operators as the key to solving problems in which they arise.

The first volume re-examines basic notions of linear algebra, including vector spaces, linear operators, duality, determinants, diagonalization, and inner product spaces. It provides an overview of linear algebra with sufficient mathematical precision for advanced use of the subject. The book offers a nice and varied selection of exercises, with examples that are well-crafted and provide a clear understanding of the methods involved. New notions are introduced with clear motivation, 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, such as generalized eigenspaces, further applications of Jordan form, and 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, as both deal with vast topics.

Overall, this two-volume set is an essential resource for graduate students seeking to deepen their understanding of linear algebra and its applications in various fields.

Weight: 1042g
Dimension: 183 x 257 x 33 (mm)
ISBN-13: 9781470461607