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The readings are assigned in: Amazon logo Strang, Gilbert. Introduction to Linear Algebra. 4th ed. Wellesley, MA: Wellesley-Cambridge Press, February 2009. ISBN: 9780980232714.


LEC #TopicsReadings
1The Geometry of Linear Equations1.1-2.1
2Elimination with Matrices2.2-2.3
3Matrix Operations and Inverses2.4-2.5
4LU and LDU Factorization2.6
5Transposes and Permutations2.7
6Vector Spaces and Subspaces3.1
7The Nullspace: Solving Ax = 03.2
8Rectangular PA = LU and Ax = b3.3-3.4
9Row Reduced Echelon Form3.3-3.4
10Basis and Dimension3.5
11The Four Fundamental Subspaces3.6
12Exam 1: Chapters 1 to 3.5
13Graphs and Networks8.2
14Orthogonality4.1
15Projections and Subspaces4.2
16Least Squares Approximations4.3
17Gram-Schmidt and A = QR4.4
18Properties of Determinants5.1
19Formulas for Determinants5.2
20Applications of Determinants5.3
21Eigenvalues and Eigenvectors6.1
22Exam Review
23Exam 2: Chapters 1-5
24Diagonalization6.2
25Markov Matrices8.3
26Fourier Series and Complex Matrices8.5, 10.2
27Differential Equations6.3
28Symmetric Matrices6.4
29Positive Definite Matrices6.5
30Matrices in Engineering8.1
31Singular Value Decomposition6.7
32Similar Matrices6.6
33Linear Transformations7.1-7.2
34Choice of Basis7.3-7.4
35Exam Review
36Exam 3: Chapters 1-8 (8.1, 2, 3, 5)
37Fast Fourier Transform10.3
38Linear Programming8.4
39Numerical Linear Algebra9.1-9.3
40Final Exams



Table of Contents




1. Introduction to Vectors


1.1 Vectors and Linear Combinations
1.2 Lengths and Dot Products



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 = LU
2.7 Transposes and Permutations



3. Vector Spaces and Subspaces


3.1 Spaces of Vectors
3.2 The Nullspace of A: Solving Ax = 0
3.3 The Rank and the Row Reduced Form
3.4 The Complete Solution to Ax = b
3.5 Independence, Basis, and Dimension
3.6 Dimensions of the Four Subspaces



4. Orthogonality


4.1 Orthogonality of the Four Subspaces
4.2 Projections
4.3 Least Squares Approximations
4.4 Orthogonal 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 Applications to Differential Equations
6.4 Symmetric Matrices
6.5 Positive Definite Matrices
6.6 Similar Matrices
6.7 The Singular Value Decomposition (SVD)



7. Linear Transformations


7.1 The Idea of a Linear Transformation
7.2 The Matrix of a Linear Transformation
7.3 Change of Basis
7.4 Diagonalization and the Pseudoinverse



8. Applications


8.1 Matrices in Engineering
8.2 Graphs and Networks
8.3 Markov Matrices and Economic Models
8.4 Linear Programming
8.5 Fourier Series: Linear Algebra for Functions
8.6 Computer Graphics



9. Numerical Linear Algebra


9.1 Gaussian Elimination in Practice
9.2 Norms and Condition Numbers
9.3 Iterative Methods for Linear Algebra



10. Complex Vectors and Complex Matrices


10.1 Complex Numbers
10.2 Hermitian and Unitary Matrices
10.3 The Fast Fourier Transform


 








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