Book:Gilbert Strang/Introduction to Linear Algebra/Fifth Edition

Gilbert Strang: Introduction to Linear Algebra (5th Edition)

Published $\text {2016}$

Subject Matter

• Linear Algebra

Contents

1 Introduction to Vectors

1.1 Vectors and Linear Combinations

1.2 Lengths and Dot Products

1.3 Matrices

2 Solving Linear Equations

2.1 Vectors and Linear Equations

2.2 The Idea of Elimination

2.3 Elimination Using Matrices

2.4 Rules for Matrix Operations

2.5 Inverse Matrices

2.6 Elimination = Factorization: $A = L U$

2.7 Transposes and Permutations

3 Vector Spaces and Subspaces

3.1 Spaces of Vectors

3.2 The Nullspace of A: Solving $A x = 0$ and $R x = 0$

3.3 The Complete Solution to $A x = b$

3.4 Independence, Basis and Dimension

3.5 Dimensions of the Four Subspaces

4 Orthogonality

4.1 Orthogonality of the Four Subspaces

4.2 Projections

4.3 Least Squares Approximations

4.4 Orthonormal Bases and Gram-Schmidt

5 Determinants

5.1 The Properties of Determinants

5.2 Permutations and Cofactors

5.3 Cramer’s Rule, Inverses, and Volumes

6 Eigenvalues and Eigenvectors

6.1 Introduction to Eigenvalues

6.2 Diagonalizing a Matrix

6.3 Systems of Differential Equations

6.4 Symmetric Matrices

6.5 Positive Definite Matrices

7 The Singular Value Decomposition (SVD)

7.1 Image Processing by Linear Algebra

7.2 Bases and Matrices in the SVD

7.3 Principal Component Analysis (PCA by the SVD)

7.4 The Geometry of the SVD

8 Linear Transformations

8.1 The Idea of a Linear Transformation

8.2 The Matrix of a Linear Transformation

8.3 The Search for a Good Basis

9 Complex Vectors and Matrices

9.1 Complex Numbers

9.2 Hermitian and Unitary Matrices

9.3 The Fast Fourier Transform

10 Applications

10.1 Graphs and Networks

10.2 Matrices in Engineering

10.3 Markov Matrices, Population, and Economics

10.4 Linear Programming

10.5 Fourier Series: Linear Algebra for Functions

10.6 Computer Graphics

10.7 Linear Algebra for Cryptography

11 Numerical Linear Algebra

11.1 Gaussian Elimination in Practice

11.2 Norms and Condition Numbers

11.3 Iterative Methods and Preconditioners

12 Linear Algebra in Probability & Statistics

12.1 Mean, Variance, and Probability

12.2 Covariance Matrices and Joint Probabilities

12.3 Multivariate Gaussian andWeighted Least Squares

Matrix Factorizations

Index

Six Great Theorems / Linear Algebra in a Nutshell

Further Editions

• 1993: Gilbert Strang: Introduction to Linear Algebra
• 2009: Gilbert Strang: Introduction to Linear Algebra (4th ed.)