Linear Algebra 3 Edition |
|||||||||||||

Author: G. Strang | |||||||||||||

Index Code : Science.Mathematics.LinearAlgebra |
|||||||||||||

Example Code |
|||||||||||||

Chapters / Sections |
Examples |
||||||||||||

1. Introduction to Vectors | |||||||||||||

1.1 Vectors and Linear Combinations | A | B | |||||||||||

1.2 Lengths and Dot Products | 1 | 2 | 3 | 4 | 5 | 6 | A | B | |||||

2. Solving Linear Equations | |||||||||||||

2.1 Vectors and Linear Equations | 1 | A | B | ||||||||||

2.2 The Idea of Elimination | 1 | 2 | 3 | A | B | ||||||||

2.3 Elimination Using Matrices | 1 | 2 | A | B | C | ||||||||

2.4 Rules for Matrix Operations | 1 | 2 | 3 | 4 | A | B | C | ||||||

2.5 Inverse Matrices | 1 | 2 | 3 | 4 | 5 | A | B | ||||||

2.6 Elimination = Factorization : A = LU | 1 | 2 | 3 | A | B | ||||||||

2.7 Transpose and Permutations | 1 | 2 | 3 | 4 | A | B | |||||||

3. Vector Spaces and Subspace | |||||||||||||

3.1 Spaces of Vectors | 1 | 2 | 3 | 4 | 5 | A | B | ||||||

3.2 The Nullspace of A: Solving Ax = 0 | 1 | 2 | 3 | 4 | A | B | |||||||

3.3 The Rank and the Row Reduced Form | 1 | 2 | A | B | |||||||||

3.4 The Complete Solution to Ax = b | 1 | 2 | A | B | C | ||||||||

3.5 Independence, Basis and Dimension | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | ||

3.6 Dimensions of the Four Subspaces | 1 | 2 | A | B | |||||||||

4. Orthogonality | |||||||||||||

4.1 Orthogonality of the Four Subspaces | 1 | 2 | 3 | 4 | 5 | A | B | ||||||

4.2 Projections | 1 | 2 | 3 | A | B | ||||||||

4.3 Least Squares Approximations | 1 | 2 | 3 | A | B | ||||||||

4.4 Orthogonal Bases and Gram-Schmidt | 1 | 2 | 3 | 4 | 5 | A | |||||||

5. Determinant | |||||||||||||

5.1 The Properties of Determinants | A | B | |||||||||||

5.2 Permutations and Cofactors | 1 | 2 | 3 | 4 | 5 | 6 | 7 | A | B | ||||

5.3 Cramer's Rule, Inverse, and Volumes | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | A | B | |

6. Eigenvalues and Eigenvectors | |||||||||||||

6.1 Introduction to Eigenvalues | 1 | 2 | 3 | 4 | A | B | |||||||

6.2 Diagonalizing a Matrix | 1 | 2 | 3 | A | B | ||||||||

6.3 Applications to Differential Equations | 1 | 2 | 3 | 4 | 5 | 6 | A | B | |||||

6.4 Symmetric Matrices | 1 | 2 | 3 | 4 | A | ||||||||

6.5 Positive Definite Matrices | 1 | 2 | 3 | 4 | 5 | 6 | 7 | A | B | ||||

6.6 Similar Matrices | 1 | 2 | 3 | 4 | A | B | |||||||

6.7 Singular Value Decomposition (SVD) | 1 | 2 | A | ||||||||||

7. Linear Transformation | |||||||||||||

7.1 The Idea of a Linear Transformation | 1 | 2 | 3 | 4 | 5 | 6 | A | B | |||||

7.2 The Matrix of a Linear Transformation | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | A | B | |

7.3 Change of Basis | 1 | 2 | 3 | A | |||||||||

7.4 Diagonalization and the Pseudoinverse | 1 | 2 | 3 | 4 | A | ||||||||

8. Applications | |||||||||||||

8.1 Matrices in Engineering | 1 | 2 | |||||||||||

8.2 Graphs and Networks | 1 | ||||||||||||

8.3 Markov Matrices and Economic Models | 1 | 2 | 3 | 4 | 5 | ||||||||

8.4 Linear Programming | 1 | 2 | |||||||||||

8.5 Fourier Series: Linear Algebra for Functions | 1 | 2 | 3 | ||||||||||

8.6 Computer Graphics | |||||||||||||

9. Numerical Linear Algebra | |||||||||||||

9.1 Gaussian Elimination in Practice | |||||||||||||

9.2 Norms and Condition Numbers | 1 | 2 | 3 | 4 | |||||||||

9.3 Iterative Methods for Linear Algebra | 1 | ||||||||||||

10.Complex Vectors and Matrices | |||||||||||||

10.1 Complex Numbers | 1 | ||||||||||||

10.2 Hermitian and Unitary Matrices | 1 | 2 | 3 | ||||||||||

10.3 The Fast Fourier Transform | 1 |