Linear Algebra is a text for a first US undergraduate Linear Algebra course. It is Free. You can use it as a main text, as a supplement, or for independent study.
Welcome to this online course on Linear Algebra.
Linear Algebra is a branch of mathematics that plays a fundamental to role in many parts of Science and Engineering, such as Quantum Mechanics, Coding Theory, Signal Processing and Control Theory .
As Linear Algebra is a common component of many university programmes in Science or Engineering, this course can be used as additional study or preparation for on campus courses on Linear Algebra. Please note that we cannot guarantee that this course can replace an on campus course.
The course has no preliminaries other than basic high school mathematics. Furthermore, the course is self contained; it can be studied without extra resources. Nevertheless, for each topic you can find some references to standard literature that you can consult for further reading.
This 16-minute video lesson shows that a projection onto a subspace is a linear transformation. [Linear Algebra playlist: Lesson 110 of 143]
This is a communication intensive supplement to Linear Algebra (18.06). The main emphasis is on the methods of creating rigorous and elegant proofs and presenting them clearly in writing.
This 14-minute video lesson shows how to determine the equation for a plane in R3 using a point on the plane and a normal vector.
This 25-minute video lesson introduces the idea of an angle between two vectors.
This 19-minute video lesson provides dot and cross product comparison and Intuition.
This 27-minute video lesson provides an example using the orthogonal change-of-basis matrix to find the transformation matrix. [Linear Algebra playlist: Lesson 128 of 143]
This 17-minute video lesson shows how to express a projection on to a line as a Matrix Vector prod. [Linear Algebra playlist: Lesson 61 of 143]
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.
This 15-minute video lesson shows how to find the eigenvectors and eigenspaces of a 2x2 matrix. [Linear Algebra playlist: Lesson 136 of 143]
This 12-minute video lesson provides an introduction to the null space of a matrix and shows that the null space of a matrix is a valid subspace. [Linear Algebra playlist: Lesson 34 of 143]
This 18-minute video lesson shows how to solve a system of linear equations by putting an augmented matrix into reduced row echelon form. [Linear Algebra playlist: Lesson 30 of 143]
This 12-minute video lesson provides another example of solving a system of linear equations by putting an augmented matrix into reduced row echelon form. [Linear Algebra playlist: Lesson 32 of 143]
This 10-minute video lesson shows how to figure out a normal vector to a plane from its equation. [Linear Algebra playlist: Lesson 141 of 143]
This 13-minute video lesson shows how to calculate the null space of a matrix. [Linear Algebra playlist: Lesson 35 of 143]
This 12-minute video lesson discusses how to understand how the null space of a matrix relates to the linear independence of its column vectors. [Linear Algebra playlist: Lesson 36 of 143]
This 12-minute video lesson finds that the orthogonal complement of the orthogonal complement of V is V. [Linear Algebra playlist: Lesson 103 of 143]
This 11-minute video lesson shows that orthogonal matrices preserve angles and lengths. [Linear Algebra playlist: Lesson 129 of 143]
This 17-minute vidoe lesson shows proof of the Cauchy-Schwarz Inequality.