Linear Algebra

Resource Index

« Previous »

This resource index gives users access to most of the course resources in a single location.

Unit I: Ax = b and the Four Subspaces

TITLES	LECTURE VIDEOS	LECTURE NOTES	TEXTBOOK READINGS	PROBLEM SOLVING VIDEOS	PROBLEM SETS
The Geometry of Linear Equations	The Geometry of Linear Equations	Lecture summary (PDF)	Sections 1.1, 1.2, and 2.1 in the 4th or 5th edition	Geometry of Linear Algebra 线性代数的几何表示	Problems (PDF) Solutions (PDF)
An Overview of Key Ideas	An Overview of Linear Algebra	Lecture summary (PDF)	Sections 1.3 in the 4th or 5th edition	An Overview of Key Ideas	None
Elimination with Matrices	Lecture: Elimination with Matrices	Lecture summary (PDF)	Section 2.2 through 2.3 in the 4th or 5th edition	Recitation: Elimination with Matrices	Problems (PDF) Solutions (PDF)
Multiplication and Inverse Matrices	Multiplication and Inverse Matrices	Lecture summary (PDF)	Section 2.4 through 2.5 in the 4th or 5th edition	Inverse Matrices	Problems (PDF) Solutions (PDF)
Factorization into A = LU	Factorization into A = LU	Lecture summary (PDF)	Section 2.6 in the 4th or 5th edition	LU Decomposition	Problems (PDF) Solutions (PDF)
Transposes, Permutations, Vector Spaces	Transposes, Permutations, Vector Spaces	Lecture summary (PDF)	Section 2.7 in the 4th or 5th edition	Subspaces of Three Dimensional Space 三维空间的子空间	Problems (PDF) Solutions (PDF)
Column Space and Nullspace	Column Space and Nullspace	Lecture summary (PDF)	Section 3.1 through 3.2 in the 4th or 5th edition	Vector Subspaces	Problems (PDF) Solutions (PDF)
Solving Ax = 0: Pivot Variables, Special Solutions	Solving Ax = 0: Pivot Variables, Special Solutions	Lecture summary (PDF)	Section 3.2 in the 4th or 5th edition	Solving Ax=0	Problems (PDF) Solutions (PDF)
Solving Ax = b: Row Reduced Form R	Solving Ax = b: Row Reduced Form R	Lecture summary (PDF)	Section 3.3 through 3.4 in the 4th or 5th edition	Solving Ax=b	Problems (PDF) Solutions (PDF)
Independence, Basis and Dimension	Independence, Basis and Dimension	Lecture summary (PDF)	Section 3.5 in the 4th edition or Section 3.4 in the 5th edition	Basis and Dimension	Problems (PDF) Solutions (PDF)
The Four Fundamental Subspaces	The Four Fundamental Subspaces	Lecture summary (PDF)	Section 3.6 in the 4th edition or Section 3.5 in the 5th edition	Computing the Four Fundamental Subspaces	Problems (PDF) Solutions (PDF)
Matrix Spaces; Rank 1; Small World Graphs	Matrix Spaces; Rank 1; Small World Graphs	Lecture summary (PDF)	Section 3.3 and 8.2 in the 4th edition or Section 3.3 and 10.1 in the 5th edition	Matrix Spaces	Problems (PDF) Solutions (PDF)
Graphs, Networks, Incidence Matrices	Graphs, Networks, Incidence Matrices	Lecture summary (PDF)	Section 8.2 in the 4th edition or Section 10.1 in the 5th edition	Graphs and Networks	Problems (PDF) Solutions (PDF)
Exam 1 Review	Exam 1 Review	Lecture summary (PDF)	Review Chapters 1, 2, and 3, plus Section 8.2 in the 4th edition or Chapters 1, 2, and 3, plus Section 10.1 in the 5th edition	Exam 1 Problem Solving	None

Exam 1

EXAM	EXAMS AND SOLUTIONS
Exam 1	Exams (PDF) Solutions (PDF)

Unit II: Least Squares, Determinants and Eigenvalues

TITLES	LECTURE VIDEOS	LECTURE NOTES	TEXTBOOK READINGS	PROBLEM SOLVING VIDEOS	PROBLEM SETS
Orthogonal Vectors and Subspaces	Orthogonal Vectors and Subspaces	Lecture summary (PDF)	Section 4.1 in the 4th or 5th edition	Problem Solving: Orthogonal Vectors and Subspaces	Problems (PDF) Solutions (PDF)
Projections onto Subspaces	Lecture 15: Projections onto Subspaces	Lecture summary (PDF)	Section 4.2 in the 4th or 5th edition	Problem Solving: Projection onto Subspaces	Problems (PDF) Solutions (PDF)
Projection Matrices and Least Squares	Lecture 16: Projection Matrices and Least Squares	Lecture summary (PDF)	Section 4.3 in the 4th or 5th edition	Problem Solving: Least Squares Approximation	Problems (PDF) Solutions (PDF)
Orthogonal Matrices and Gram-Schmidt	Lecture 17: Orthogonal Matrices and Gram-Schmidt	Lecture summary (PDF)	Section 4.4 in the 4th or 5th edition	Problem Solving: Gram-Schmidt Orthogonalization	Problems (PDF) Solutions (PDF)
Properties of Determinants	Lecture 18: Properties of Determinants	Lecture summary (PDF)	Section 5.1 in the 4th or 5th edition	Problem Solving: Properties of Determinants	Problems (PDF) Solutions (PDF)
Determinant Formulas and Cofactors	Lecture 19: Determinant Formulas and Cofactors	Lecture summary (PDF)	Section 5.2 in the 4th or 5th edition	Problem Solving: Determinants 行列式	Problems (PDF) Solutions (PDF)
Cramer’s Rule, Inverse Matrix and Volume	Lecture 20: Cramer’s Rule, Inverse Matrix and Volume	Lecture summary (PDF)	Section 5.3 in the 4th or 5th edition	Problem Solving: Determinants and Volume 行列式和体积	Problems (PDF) Solutions (PDF)
Eigenvalues and Eigenvectors	Lecture 21: Eigenvalues and Eigenvectors	Lecture summary (PDF)	Section 6.1 through 6.2 in the 4th or 5th edition	Problem Solving: Eigenvalues and Eigenvectors	Problems (PDF) Solutions (PDF)
Diagonalization and Powers of A	Lecture 22: Diagonalization and Powers of A	Lecture summary (PDF)	Section 6.2 in the 4th or 5th edition	Problem Solving: Powers of a Matrix	Problems (PDF) Solutions (PDF)
Differential Equations and exp(At)	Lecture 23: Differential Equations and exp(At)	Lecture summary (PDF)	Section 6.3 in the 4th or 5th edition	Problem Solving: Determinants and VolumeDifferential Equations and exp(At) 微分方程指数矩阵(At)	Problems (PDF) Solutions (PDF)
Markov Matrices; Fourier Series	Lecture 24: Markov Matrices; Fourier Series	Lecture summary (PDF)	Section 8.3 and 8.5 in the 4th edition or Sections 10.3 and 10.5 in the 5th edition	Problem Solving: Markov Matrices	Problems (PDF) Solutions (PDF)
Exam 2 Review	Exam 2 Review	Lecture summary (PDF)	Review Chapters 4, 5, and 6 (through Sec. 6.3) plus Sections 8.3 and 8.5 in the 4th edition or Review Chapters 4, 5, and 6 (through Sec. 6.3) plus Sections 10.3 and 10.5 in the 5th edition	Exam 2 Problem Solving 第二次考试例题	None

Exam 2

EXAM	EXAMS AND SOLUTIONS
Exam 2	Exams (PDF) Solutions (PDF)

Unit III: Positive Definite Matrices and Applications

TITLES	LECTURE VIDEOS	LECTURE NOTES	TEXTBOOK READINGS	PROBLEM SOLVING VIDEOS	PROBLEM SETS
Symmetric Matrices and Positive Definiteness	Lecture 25: Symmetric Matrices and Positive Definiteness	Lecture summary (PDF)	Section 6.4 through 6.5 in the 4th or 5th edition	Problem Solving: Symmetric Matrices and Positive Definiteness	Problems (PDF) Solutions (PDF)
Complex Matrices; Fast Fourier Transform (FFT)	Lecture 26: Complex Matrices; Fast Fourier Transform (FFT)	Lecture summary (PDF)	Section 10.2 through 10.3 in the 4th edition or Section 9.2 and 9.3 in the 5th edition	Problem Solving: Complex Matrices	Problems (PDF) Solutions (PDF)
Positive Definite Matrices and Minima	Lecture 27: Positive Definite Matrices and Minima	Lecture summary (PDF)	Section 6.5 in the 4th or 5th edition	Problem Solving: Positive Definite Matrices and Minima	Problems (PDF) Solutions (PDF)
Similar Matrices and Jordan Form	Lecture 28: Similar Matrices and Jordan Form	Lecture summary (PDF)	Section 6.6 in the 4th edition or Section 6.2 in the 5th edition	Problem Solving: Similar Matrices	Problems (PDF) Solutions (PDF)
Singular Value Decomposition	Lecture 29: Singular Value Decomposition	Lecture summary (PDF)	Section 6.7 in the 4th edition or Section 7.1 and 7.2 in the 5th edition	Problem Solving: Determinants and VolumeComputing the Singular Value Decomposition	Problems (PDF) Solutions (PDF)
Linear Transformations and their Matrices	Lecture 30: Linear Transformations and their Matrices	Lecture summary (PDF)	Section 7.1 in the 4th edition or Section 8.1 in the 5th edition	Problem Solving: Linear Transformations	Problems (PDF) Solutions (PDF)
Change of Basis; Image Compression	Lecture 31: Change of Basis; Image Compression	Lecture summary (PDF)	Section 7.2 in the 4th edition or Section 8.2 in the 5th edition	Problem Solving: Change of Basis	Problems (PDF) Solutions (PDF)
Left and Right Inverses; Pseudoinverse	Lecture 33: Left and Right Inverses; Pseudoinverse	Lecture summary (PDF)	Section 7.3 in the 4th edition or Section 8.3 in the 5th edition	Problem Solving: Pseudoinverses	Problems (PDF) Solutions (PDF)
Exam 3 Review	Exam 3 Review	Lecture summary (PDF)	Review Chapters 6 and 7, plus Sections 10.2 through 10.3 in the 4th edition or Review Chapters 6, 7, and 8 plus Sections 9.2 through 9.3 in the 5th edition	Exam 3 Problem Solving	None

Exam 3

EXAM	EXAMS AND SOLUTIONS
Exam 3	Exams (PDF) Solutions (PDF)

Final Course Review

TITLES	LECTURE VIDEOS	LECTURE NOTES	TEXTBOOK READINGS	PROBLEM SOLVING VIDEOS	PROBLEM SETS
Final Course Review	Final Course Review	Lecture summary (PDF)	None	Final Exam Problem Solving	None

Final Exam

FINAL EXAM	EXAMS AND SOLUTIONS
Final Exam	Exams (PDF) Solutions (PDF)

« Previous »