Advanced Linear Algebra (Textbooks in Mathematics) 2nd Edition by Bruce Cooperstein (PDF)

Description

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 algebraAdds sections on normed vector spaces, orthogonal spaces over perfect fields of characteristic two, and Clifford algebrasIncludes several new exercises and examples, with a solutions manual available upon qualifying course adoptionThe book shows students the beauty of linear algebra while preparing them for further study in mathematics.

User’s Reviews

Editorial Reviews: Review “This is the substantially extended second edition of a book comprising an advanced course in linear algebra …”―Zentralblatt MATH 1319Praise 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 About the Author Bruce Cooperstein is a professor of mathematics at the University of California, Santa Cruz, USA. He was a visiting scholar at the Carnegie Foundation for the Advancement of Teaching (spring 2007) and a recipient of the Kellogg National Fellowship (1982–1985) and the Pew National Fellowship for Carnegie Scholars (1999–2000). Dr. Cooperstein has authored numerous papers in refereed mathematics journals.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I just received the text and started reading it with great pleasure.It is a no nonsense book and assumes you know something, but at the same time starts off giving you basic knowledge and builds to more advanced topics in an orderly way.One of the great features of this book is that every section starts with a “What You Need to Know “ section that lists the concepts used in the section and gives references to texts that can help you fill in any gaps in your knowledge.There are two other features that I like in a math textbook. There is a section on answers to selected problems and a section on hints for solving selected problems. I do mainly self-study, so this gives a way of finding out if you’re really as smart as you think you are, or just a helping hand when you get stuck.The book is very clearly written, but does not belabor points the author makes or go into a great deal of explanation. Many pages are simply theorem-proof-theorem-proof. This is fine, since this is billed as an advanced text.The layout of the book is Spartan with little time or space spent on making a beautiful presentation. The effort has gone to readable type, good sized print and a great deal of information. It delivers a good learning experience.I like this book!

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