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Advanced Linear Algebra

By: Bruce Cooperstein

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Paperback | 14 October 2024 | Edition Number 2

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Advanced Linear Algebra, Second Edition takes a gentle approach that starts with familiar concepts and then gradually builds to deeper results. Each section begins with an outline of previously introduced concepts and results necessary for mastering the new material. By reviewing what students need to know before moving forward, the text builds a solid foundation upon which to progress.

The new edition of this successful text focuses on vector spaces and the maps between them that preserve their structure (linear transformations). Designed for advanced undergraduate and beginning graduate students, the book discusses the structure theory of an operator, various topics on inner product spaces, and the trace and determinant functions of a linear operator. It addresses bilinear forms with a full treatment of symplectic spaces and orthogonal spaces, as well as explains the construction of tensor, symmetric, and exterior algebras.

Featuring updates and revisions throughout, Advanced Linear Algebra, Second Edition:

Contains new chapters covering sesquilinear forms, linear groups and groups of isometries, matrices, and three important applications of linear algebra
Adds sections on normed vector spaces, orthogonal spaces over perfect fields of characteristic two, and Clifford algebras
Includes several new exercises and examples, with a solutions manual available upon qualifying course adoption

The book shows students the beauty of linear algebra while preparing them for further study in mathematics.

Industry Reviews

"This is the substantially extended second edition of a book comprising an advanced course in linear algebra ..."
-Zentralblatt MATH 1319

Praise for the First Edition:"The book is well written, and the examples are appropriate. ... Each section contains relevant problems at the end. The 'What You Need to Know' feature at the beginning of each section outlining the knowledge required to grasp the material is useful. Summing Up: Recommended."
-CHOICE, January 2011

"Pedagogically, a structural and general approach is taken, and topically, the material has been chosen in order to cover the material a beginning graduate student would be expected to know when taking a first course in group or field theory or functional analysis."
-SciTech Book News, February 2011

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