Course18.06SC158 lectures75 h 12 min
Linear Algebra
Prof. Gilbert Strang · Massachusetts Institute of Technology
About
This course covers matrix theory and linear algebra, emphasizing topics useful in other disciplines such as physics, economics and social sciences, natural sciences, and engineering. It parallels the combination of theory and applications in Professor Strang’s textbook Introduction to Linear Algebra.
Course Format
This course has been designed for independent study. It provides everything you will need to understand the concepts covered in the course. The materials include:
A complete set of Lecture Videos by Professor Gilbert Strang.
Summary Notes for all videos along with suggested readings in Prof. Strang’s textbook Linear Algebra.
Problem Solving Videos on every topic taught by an experienced MIT Recitation Instructor.
Problem Sets to do on your own with Solutions to check your answers against when you’re done.
A selection of Java® Demonstrations to illustrate key concepts.
A full set of Exams with Solutions, including review material to help you prepare.
Lectures
Syllabus
Instructor Insights
The Geometry of Linear Equations
An Overview of Key Ideas
Elimination with Matrices
Multiplication and Inverse Matrices
Factorization into A = LU
Transposes, Permutations, Vector Spaces
Column Space and Nullspace
Solving Ax = 0: Pivot Variables, Special Solutions
Solving Ax = b: Row Reduced Form R
Independence, Basis and Dimension
The Four Fundamental Subspaces
Matrix Spaces; Rank 1; Small World Graphs
Graphs, Networks, Incidence Matrices
Exam 1 Review
Orthogonal Vectors and Subspaces
Projections onto Subspaces
Projection Matrices and Least Squares
Orthogonal Matrices and Gram-Schmidt
Properties of Determinants
Determinant Formulas and Cofactors
Cramer's Rule, Inverse Matrix and Volume
- Lecture 20: Cramer's Rule, Inverse Matrix and Volume
- Problem Solving: Determinants and Volume
- 行列式和体积
Eigenvalues and Eigenvectors
Diagonalization and Powers of A
Differential Equations and exp(At)
- Lecture 23: Differential Equations and exp(At)
- Problem Solving: Differential Equations and exp(At)
- 微分方程指数矩阵(At)
Markov Matrices; Fourier Series
Exam 2 Review
Symmetric Matrices and Positive Definiteness
- Lecture 25: Symmetric Matrices and Positive Definiteness
- Problem Solving: Symmetric Matrices and Positive Definiteness
Complex Matrices; Fast Fourier Transform (FFT)
Positive Definite Matrices and Minima
- Lecture 27: Positive Definite Matrices and Minima
- Problem Solving: Positive Definite Matrices and Minima
Similar Matrices and Jordan Form
Singular Value Decomposition
- Lecture 29: Singular Value Decomposition
- Problem Solving: Computing the Singular Value Decomposition
Linear Transformations and their Matrices
Change of Basis; Image Compression
Left and Right Inverses; Pseudoinverse
Exam 3 Review
Final Course Review
Final 18.06 Lecture 2023
Resource Index
- The Geometry of Linear Equations
- Geometry of Linear Algebra
- 线性代数的几何表示
- An Overview of Linear Algebra
- An Overview of Key Ideas
- Lecture: Elimination with Matrices
- Elimination with Matrices
- Multiplication and Inverse Matrices
- Inverse Matrices
- Factorization into A = LU
- LU Decomposition
- Transposes, Permutations, Vector Spaces
- Subspaces of Three Dimensional Space
- 三维空间的子空间
- Column Space and Nullspace
- Vector Subspaces
- Solving Ax = 0: Pivot Variables, Special Solutions
- Solving Ax=0
- Solving Ax = b: Row Reduced Form R
- Solving Ax=b
- Independence, Basis and Dimension
- Basis and Dimension
- The Four Fundamental Subspaces
- Computing the Four Fundamental Subspaces
- Matrix Spaces; Rank 1; Small World Graphs
- Matrix Spaces
- Graphs, Networks, Incidence Matrices
- Graphs and Networks
- Exam 1 Review
- Exam 1 Problem Solving
- Orthogonal Vectors and Subspaces
- Problem Solving: Orthogonal Vectors and Subspaces
- Lecture 15: Projections onto Subspaces
- Lecture 16: Projection Matrices and Least Squares
- Problem Solving: Least Squares Approximation
- Lecture 17: Orthogonal Matrices and Gram-Schmidt
- Problem Solving: Gram-Schmidt Orthogonalization
- Lecture 18: Properties of Determinants
- Problem Solving: Properties of Determinants
- Lecture 19: Determinant Formulas and Cofactors
- Problem Solving: Determinants
- 行列式
- Lecture 20: Cramer's Rule, Inverse Matrix and Volume
- Problem Solving: Determinants and Volume
- 行列式和体积
- Lecture 21: Eigenvalues and Eigenvectors
- Problem Solving: Eigenvalues and Eigenvectors
- Lecture 22: Diagonalization and Powers of A
- Problem Solving: Powers of a Matrix
- Lecture 23: Differential Equations and exp(At)
- Problem Solving: Determinants and VolumeDifferential Equations and exp(At)
- 微分方程指数矩阵(At)
- Lecture 24: Markov Matrices; Fourier Series
- Problem Solving: Markov Matrices
- Exam 2 Review
- Exam 2 Problem Solving
- 第二次考试例题
- Lecture 25: Symmetric Matrices and Positive Definiteness
- Problem Solving: Symmetric Matrices and Positive Definiteness
- Lecture 26: Complex Matrices; Fast Fourier Transform (FFT)
- Problem Solving: Complex Matrices
- Lecture 27: Positive Definite Matrices and Minima
- Problem Solving: Positive Definite Matrices and Minima
- Lecture 28: Similar Matrices and Jordan Form
- Problem Solving: Similar Matrices
- Lecture 29: Singular Value Decomposition
- Problem Solving: Determinants and VolumeComputing the Singular Value Decomposition
- Lecture 30: Linear Transformations and their Matrices
- Problem Solving: Linear Transformations
- Lecture 31: Change of Basis; Image Compression
- Problem Solving: Change of Basis
- Lecture 33: Left and Right Inverses; Pseudoinverse
- Problem Solving: Pseudoinverses
- Exam 3 Review
- Exam 3 Problem Solving
- Final Course Review
- Final Exam Problem Solving
Syllabus and materials
At MIT OpenCourseWare, as the course publishes them.
Credits and licence
- Institution
- Massachusetts Institute of Technology
- Department
- Mathematics
- Teacher
- Prof. Gilbert Strang
- Term
- Fall 2011
- Level
- Undergraduate
- Language
- English
- Subjects
- Mathematics
- Source
- MIT OpenCourseWare
- Licence
- CC BY-NC-SA 4.0, as MIT OpenCourseWare states it. Non-commercial use only. MIT OpenCourseWare's terms
- Attribution
- Prof. Gilbert Strang. Linear Algebra. Fall 2011. Massachusetts Institute of Technology: MIT OpenCourseWare, https://ocw.mit.edu/. License: Creative Commons BY-NC-SA.
- Who can watch
- MIT OpenCourseWare gives no rating. Invisible Network shows it to Tweens profiles and older, judged from what the source says about it. How courses are placed
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