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Taylor & Francis
Advanced Linear Algebra, Second Edition / Edition 2

Advanced Linear Algebra, Second Edition / Edition 2

by Bruce Cooperstein


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Product Details

ISBN-13: 9781482248845
Publisher: Taylor & Francis
Publication date: 05/13/2015
Series: Textbooks in Mathematics Series , #27
Edition description: Revised
Pages: 622
Product dimensions: 6.10(w) x 9.10(h) x 1.40(d)

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

Preface to the Second Edition

Preface to the First Edition


List of Figures

Symbol Description

Vector Spaces


The Space ₣n

Vector Spaces over an Arbitrary Field

Subspaces of Vector Spaces

Span and Independence

Bases and Finite-Dimensional Vector Spaces

Bases and Infinite-Dimensional Vector Spaces

Coordinate Vectors

Linear Transformations

Introduction to Linear Transformations

The Range and Kernel of a Linear Transformation

The Correspondence and Isomorphism Theorems

Matrix of a Linear Transformation

The Algebra of (V,W) and Mmn(₣)

Invertible Transformations and Matrices


The Algebra of Polynomials

Roots of Polynomials

Theory of a Single Linear Operator

Invariant Subspaces of an Operator

Cyclic Operators

Maximal Vectors

Indecomposable Linear Operators

Invariant Factors and Elementary Divisors

Canonical Forms

Operators on Real and Complex Vector Spaces

Normed and Inner Product Spaces

Inner Products

Geometry in Inner Product Spaces

Orthonormal Sets and the Gram-Schmidt Process

Orthogonal Complements and Projections

Dual Spaces


Normed Vector Spaces

Linear Operators on Inner Product Spaces

Self-Adjoint and Normal Operators

Spectral Theorems

Normal Operators on Real Inner Product Spaces

Unitary and Orthogonal Operators

The Polar Decomposition and Singular Value Decomposition

Trace and Determinant of a Linear Operator

Trace of a Linear Operator

Determinant of a Linear Operator and Matrix

Uniqueness of the Determinant of a Linear Operator

Bilinear Forms

Basic Properties of Bilinear Maps

Symplectic Spaces

Quadratic Forms and Orthogonal Space

Orthogonal Space, Characteristic Two

Real Quadratic Forms

Sesquilinear Forms and Unitary Geometry

Basic Properties of Sesquilinear Forms

Unitary Space

Tensor Products

Introduction to Tensor Products

Properties of Tensor Products

The Tensor Algebra

The Symmetric Algebra

The Exterior Algebra

Clifford Algebras, char ₣ ≠ 2

Linear Groups and Groups of Isometries

Linear Groups

Symplectic Groups

Orthogonal Groups, char ₣ ≠ 2

Unitary Groups

Additional Topics in Linear Algebra

Matrix Norms

The Moore–Penrose Inverse of a Matrix

Nonnegative Matrices

The Location of Eigenvalues

Functions of Matrices

Applications of Linear Algebra

Least Squares

Error Correcting Codes

Ranking Webpages for Search Engines


Concepts from Topology and Analysis

Concepts from Group Theory

Answers to Selected Exercises

Hints to Selected Problems



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