A first look at eigenvectors and eigenvalues. Definition, quick examples, and a theorem. More on this in part 2!Video. Notes.
Monthly Archives: November 2022
Determinants. Part 2.
Two applications/connections of determinants: the inverse of a matrix and Cramer’s rule, and eigenvectors and eigenvalues. More on the latter in a future video!Video. Notes.
Determinants. Part 1.
How are determinants defined and calculated? What are their main properties? I talk about that here and add a little example at the end on Gaussian integrals in arbitrary dimensions. Video. Notes.
Gaussian integrals and Feynman’s trick
We go over how to calculate the basic Gaussian integral and then other integrals using Feynman’s parameter differentiation approach. There will be more videos coming up on multidimensional Gaussians!Video. Notes.
Linear operators. Part 3.
Linear operators: three theorems on inverses, kernels and linear independence. Check it out! Video. Notes.
Linear operators. Part 2.
Linear operators: More examples, calculating the kernel, the image, and the inverse of small matrices and a simple differential operator.Video. Notes.
Linear operators. Part 1.
Linear operators: a first look! Definition, examples, matrix representation, image, kernel.Video. Notes.
Linear systems of equations. Part 3.
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. Part 2.
Linear systems of equations: first steps on how to solve diagonal and triangular systems. Degeneracy & consistency.Video. Notes.
Linear systems of equations. Part 1.
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.