Linear Algebra Course Introduction

This course covers matrix theory and linear algebra, emphasizing topics useful in other disciplines. Linear algebra is a branch of mathematics that studies systems of linear equations and the properties of matrices. The concepts of linear algebra are extremely useful in physics, economics and social sciences, natural sciences, and engineering. Due to its broad range of applications, linear algebra is one of the most widely taught subjects in college-level mathematics (and increasingly in high school).

18.02 Multivariable Calculus is a formal prerequisite for MIT students wishing to enroll in 18.06 Linear Algebra, but knowledge of calculus is not required to learn the subject.

To succeed in this course you will need to be comfortable with vectors, matrices, and three-dimensional coordinate systems. This material is presented in the first few lectures of 18.02 Multivariable Calculus, and again here.

The basic operations of linear algebra are those you learned in grade school – addition and multiplication to produce "linear combinations." But with vectors, we move into four-dimensional space and n-dimensional space!

After successfully completing the course, you will have a good understanding of the following topics and their applications:

- Systems of linear equations
- Row reduction and echelon forms
- Matrix operations, including inverses
- Block matrices
- Linear dependence and independence
- Subspaces and bases and dimensions
- Orthogonal bases and orthogonal projections
- Gram-Schmidt process
- Linear models and least-squares problems
- Determinants and their properties
- Cramer's Rule
- Eigenvalues and eigenvectors
- Diagonalization of a matrix
- Symmetric matrices
- Positive definite matrices
- Similar matrices
- Linear transformations
- Singular Value Decomposition

This course, designed for independent study, has been organized to follow the sequence of topics covered in an MIT course on Linear Algebra. The content is organized into three major units:

- Ax = b and the Four Subspaces
- Least Squares, Determinants and Eigenvalues
- Positive Definite Matrices and Applications

Each unit has been further divided into a sequence of sessions that cover an amount you might expect to complete in one sitting. Each session has a video lecture on the topic, accompanied by a lecture summary. For further study, there are suggested readings in Professor Strang's textbook (both the 4th and 5th editions):

Strang, Gilbert. Introduction to Linear Algebra. 4th ed. Wellesley, MA: Wellesley-Cambridge Press, February 2009. ISBN: 9780980232714

Strang, Gilbert. *Introduction to Linear Algebra*. 5th ed. Wellesley, MA: Wellesley-Cambridge Press, February 2016. ISBN: 9780980232776.

Click on the navigation links in the left column to display the sessions in the three units.

To help guide your learning, you will see how problem solving is taught by an experienced MIT Recitation instructor (six of the Problem Solving Videos are also available in Mandarin Chinese).

Finally, within each unit you will be presented with sets of problems at strategic points, so you can test your understanding of the material.

MIT expects its students to spend about 150 hours on this course. More than half of that time is spent preparing for class and doing assignments. It's difficult to estimate how long it will take you to complete the course, but you can probably expect to spend an hour or more working through each individual session.

This OCW Scholar course was developed by:

- Gilbert Strang, Professor of Mathematics, Massachusetts Institute of Technology

With technical and writing assistance from:

- Heidi Burgiel, Professor of Mathematics and Computer Science, Bridgewater State University

The Help Session Videos were developed by:

- Martina Balagovic
- Linan Chen
- Benjamin Harris
- Ana Rita Pires
- David Shirokoff
- Nikola Kamburov

To learn more about each of the TA's, visit the Meet the TAs page.