Linear Algebra and Its Applications, 4th Edition

✍ Scribed by Gilbert Strang

• Publisher: Cengage Learning
• Year: 2006
• Tongue: English
• Leaves: 542
• Edition: 4
• Category: Library

✦ Synopsis

Renowned professor and author Gilbert Strang demonstrates that linear algebra is a fascinating subject by showing both its beauty and value. While the mathematics is there, the effort is not all concentrated on proofs. Strang's emphasis is on understanding. He explains concepts, rather than deduces. This book is written in an informal and personal style and teaches real mathematics. The gears change in Chapter 2 as students reach the introduction of vector spaces. Throughout the book, the theory is motivated and reinforced by genuine applications, allowing pure mathematicians to teach applied mathematics.

✦ Table of Contents

Cover
Title Page
Contents
Preface
1 Matrices and Gaussian Elimination
1.1 Introduction
1.2 The Geometry of Linear Equations
1.3 An Example of Gaussian Elimination
1.4 Matrix Notation and Matrix Multiplication
1.5 Triangular Factors and Row Exchanges
1.6 Inverses and Transposes
1.7 Special Matrices and Applications
Review Exercises
2 Vector Spaces
2.1 Vector Spaces and Subspaces
2.2 Solving Ax = 0 and Ax = b
2.3 Linear Independence, Basis, and Dimension
2.4 The Four Fundamental Subspaces
2.5 Graphs and Networks
2.6 Linear Transformations
Review Exercises
3 Orthogonality
3.1 Orthogonal Vectors and Subspaces
3.2 Cosines and Projections onto Lines
3.3 Projections and Least Squares
3.4 Orthogonal Bases and Gram-Schmidt
3.5 The Fast Fourier Transform
Review Exercises
4 Determinants
4.1 Introduction
4.2 Properties of the Determinant
4.3 Formulas for the Determinant
4.4 Applications of Determinants
Review Exercises
5 Eigenvalues and Eigenvectors
5.1 Introduction
5.2 Diagonalization of a Matrix
5.3 Difference Equations and Powers A^k
5.4 Differential Equations and e^{At}
5.5 Complex Matrices
5.6 Similarity Transformations
Review Exercises
6 Positive Definite Matrices
6.1 Minima, Maxima, and Saddle Points
6.2 Tests for Positive Definiteness
6.3 Singular Value Decomposition
6.4 Minimum Principles
6.5 The Finite Element Method
7 Computations with Matrices
7.1 Introduction
7.2 Matrix Norm and Condition Number
7.3 Computation of Eigenvalues
7.4 Iterative Methods for Ax = b
8 Linear Programming and Game Theory
8.1 Linear Inequalities
8.2 The Simplex Method
8.3 The Dual Problem
8.4 Network Models
8.5 Game Theory
A Intersection, Sum, and Product of Spaces
A.1 The Intersection of Two Vector Spaces
A.2 The Sum of Two Vector Spaces
A.3 The Cartesian Product of Two Vector Spaces
A.4 The Tensor Product of Two Vector Spaces
A.5 The Kronecker Product A⊗B of Two Matrices
B The Jordan Form
C Matrix Factorizations
D Glossary: A Dictionary for Linear Algebra
E MATLAB Teaching Codes
F Linear Algebra in a Nutshell
Solutions to Selected Exercises
Problem Set 1.2
Problem Set 1.3
Problem Set 1.4
Problem Set 1.5
Problem Set 1.6
Problem Set 1.7
Problem Set 2.1
Problem Set 2.2
Problem Set 2.3
Problem Set 2.4
Problem Set 2.5
Problem Set 2.6
Problem Set 3.1
Problem Set 3.2
Problem Set 3.3
Problem Set 3.4
Problem Set 3.5
Problem Set 4.2
Problem Set 4.3
Problem Set 4.4
Problem Set 5.1
Problem Set 5.2
Problem Set 5.3
Problem Set 5.4
Problem Set 5.5
Problem Set 5.6
Problem Set 6.1
Problem Set 6.2
Problem Set 6.3
Problem Set 6.4
Problem Set 6.5
Problem Set 7.2
Problem Set 7.3
Problem Set 7.4
Problem Set 8.1
Problem Set 8.2
Problem Set 8.3
Problem Set 8.4
Problem Set 8.5
Problem Set A
Problem Set B