9780134860244

Linear Algebra

Arnold J. Insel, Lawrence Spence, Stephen Friedberg

5th Edition

For courses in Advanced Linear Algebra. Illustrates the power of linear algebra through practical applications This acclaimed theorem-proof text presents a careful treatment of the principal topics of linear algebra. It emphasizes the symbiotic relationship between linear transformations and matrices, but states theorems in the more general infinite-dimensional case whe

1.1

Introduction

Exercises

p.5

1.2

Vector Spaces

Exercises

p.13

1.3

Subspaces

Exercises

p.20

1.4

Linear Combinations and Systems of Linear Equations

Exercises

p.33

1.5

Linear Dependence and Linear Independence

Exercises

p.41

1.6

Bases and Dimension

Exercises

p.54

1.7

Maximal Linearly Independent Subsets

Exercises

p.62

2.1

Linear Transformations, Null Spaces, and Ranges

Exercises

p.74

2.2

The Matrix Representation of a Linear Transformation

Exercises

p.84

2.3

Composition of Linear Transformations and Matrix Multiplication

Exercises

p.96

2.4

Invertibility and Isomorphisms

Exercises

p.107

2.5

The Change of Coordinate Matrix

Exercises

p.116

2.6

Dual Spaces

Exercises

p.124

2.7

Homogeneous Linear Differential Equations with Constant Coefficients

Exercises

p.140

6.1

Inner Products and Norms

Exercises

p.334

6.2

The Gram-Schmidt Orthogonalization Process and Orthogonal Complements

Exercises

p.350

6.3

The Adjoint of a Linear Operator

Exercises

p.362

6.4

Normal and Self-Adjoint Operators

Exercises

p.371

6.5

Unitary and Orthogonal Operators and Their Matrices

Exercises

p.389

6.6

Orthogonal Projections and the Spectral Theorem

Exercises

p.400

6.7

The Singular Value Decomposition and the Pseudoinverse

Exercises

p.414

6.8

Bilinear and Quadratic Forms

Exercises

p.443

6.9

Einstein's Special Theory of Relativity

Exercises

p.456

6.10

Conditioning and the Rayleigh Quotient

Exercises

p.464

6.11

The Geometry of Orthogonal Operations

Exercises

p.471