Advanced Linear Algebra

by Bruce Cooperstein

Overview

This book discusses structure theory of an operator, topics on inner product spaces, and 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 construction of tensor, symmetric, and exterior algebras. Featuring several new exercises, the second edition adds coverage of sesquilinear forms, linear groups, matrices, normed vector spaces, orthogonal spaces over perfect fields of characteristic two, and Clifford algebras. A solutions manual is available upon qualifying course adoption.

Product Details

ISBN-13:	9781040055748
Publisher:	CRC Press
Publication date:	12/16/2015
Series:	Textbooks in Mathematics
Sold by:	Barnes & Noble
Format:	eBook
Pages:	622
File size:	968 KB

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.

Table of Contents

Vector Spaces. Linear Transformations. Polynomials. Theory of a Single Linear Operator. Normed and Inner Product Spaces. Linear Operators on Inner Product Spaces. Trace and Determinant of a Linear Operator. Bilinear Forms. Sesquilinear Forms and Unitary Geometry. Tensor Products. Linear Groups and Groups of Isometries. Additional Topics in Linear Algebra. Applications of Linear Algebra. Appendices.

What People are Saying About This

From the Publisher

… 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

Editorial 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

"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

From the Publisher