Linear Algebra is a type of mathematics that is used in advanced game development, statistical programming, mathematical programming, and more. It is also a required class in many college degrees.

We have released a 20-hour Linear Algebra course on the YouTube channel. The course is taught by Dr. Jim Hefferon, who is a professor of mathematics at St Michael's College.

Dr. Hefferon also wrote a Linear Algebra textbook, which you can download for free from a link in the video description. The video course follows along with the textbook.

This course helps students master the material of a standard US undergraduate course in Linear Algebra. The course covers subjects such as:

  • Gaussian reduction,
  • vector spaces,
  • linear maps,
  • determinants,
  • and eigenvalues and eigenvectors.

The course takes a developmental approach. It emphasizes motivation and naturalness, using many examples.

To get the most out of this course, make sure to work through the practice problems in the book in addition to watching the video.

Here is the full list of topics covered in this course:

  • Solving Linear Systems
  • Describing Solution Sets
  • General = Particular + Homogeneous
  • Vectors in Space
  • Vector Length and Angle Measure
  • Gauss-Jordan Elimination
  • The Linear Combination Lemma
  • Vector Spaces
  • Subspaces
  • Linear Independence
  • Basis
  • Dimension
  • Vector Spaces and Linear Systems
  • Isomorphism
  • Dimension Characterizes Isomorphism
  • Homomorphism
  • Range Space and Null Space
  • Extra Transformations of the Plane
  • Representing Linear Maps
  • Any Matrix Represents a Linear Map
  • Sums and Scalar Products of Matrices
  • Matrix Multiplication
  • Mechanics of Matrix Multiplication
  • Matrix Inverse
  • Changing Vector Representations
  • Changing Map Representations
  • Projection
  • Determinants
  • Permutation Expansion
  • Geometry of Determinants
  • Laplace's formula for the determinant
  • Complex Vector Spaces
  • Similarity
  • Diagonalizability
  • Eigenvalues and Eigenvectors
  • Geometry of Eigenvalues and Eigenvectors

Watch the full course (and find the link to the free book) on the YouTube channel (20-hour watch in 2 parts).