Linear operators: three theorems on inverses, kernels and linear independence. Check it out!

Video. Notes.

Linear operators: More examples, calculating the kernel, the image, and the inverse of small matrices and a simple differential operator.
Video. Notes.

Linear operators: a first look! Definition, examples, matrix representation, image, kernel.
Video. Notes.

Linear systems of equations: a first look at determinants (in 2×2 systems) and an explanation of Gaussian elimination.
Video. Notes.

Linear systems of equations: first steps on how to solve diagonal and triangular systems. Degeneracy & consistency.
Video. Notes.

Linear systems of equations: very brief and intuitive intro to some generalities like homogeneous vs inhomogeneous systems, when to expect unique or infinitely many solutions, etc. Check out part 2!
Here’s the video.
Notes here.

In this video I introduce a few of the most important matrix types and properties. More on this in upcoming videos!
Notes here.

Computational cost of vector-vector, matrix-vector, and matrix-matrix multiplication.
Video here and notes.

Matrix-vector and matrix-matrix multiplication: elementary mechanics. More on this in upcoming videos!
Check out the video and the notes.

Discussion of the meaning of coordinates of a vector and basis change, including an example in R2 and an example with polynomials.

Check out the video and the notes.