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**Linear Algebra and Its Applications (Fourth Edition) ** written by ** Gilbert Strang **
This is an other great mathematics book cover the following topics.

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: Chapter 1

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: Chapter 2

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: Chapter 3

4.1 Introduction

4.2 Properties of the Determinant

4.3 Formulas for the Determinant

4.4 Applications of Determinants

Review Exercises: Chapter 4

5.1 Introduction 233

5.2 Diagonalization of a Matrix

5.3 Difference Equations and Powers Ak

5.4 Differential Equations and eAt

5.5 Complex Matrices 280

5.6 Similarity Transformations

Review Exercises: Chapter 5

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

7.1 Introduction

7.2 Matrix Number

7.3 Computation of Eigenvalues

7.4 Iterative Methods for Ax = b

8.1 Linear Inequalities

8.2 The Simplex Method

8.3 The Dual Problem

8.4 Network Models

8.5 Game Theory

INTERSECTION, SUM, AND PRODUCT OF SPACES

THE JORDAN FORM

Solutions to Selected Exercises

Matrix Factorizations

Glossary

MATLAB Teaching Codes

Index

Linear Algebra in a Nutshell

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