Category Archives: Linear algebra

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.

I show how to use the inner product to orthogonalize monomials and obtain the Hermite polynomials as a result, using Gram-Schmidt orthogonalization.Details on Gaussian integrals and more on the Feynman trick in a future issue. Check out the video and the notes.

Definition of orthogonal bases. This video goes beyond vector spaces, using the inner product to define orthogonal bases in spaces of common vectors and functions.Check out the video here and the notes.

Definition and properties of the inner product.Check out the video and PDF.