A first look at the Dirac delta and an application with Green’s functions. Video. Notes.
Category Archives: Linear algebra
Eigensystems and Inverses. Part 2.
Recap of Part 1. Orthogonality and completeness relations. What do they look like in the infinite-dimensional case of part 1? Video. Notes.
Eigensystems and Inverses
Spectral representation of the inverse of a matrix. An example in infinite dimensions and… a first appearance of a Green’s function! Video. Notes.
Eigenvectors and Eigenvalues. Part 2.
Remider of part 1. Matrix diagonalization. Spectral representation. Similarity transformations. Two applications. Video. Notes.
Eigenvectors and Eigenvalues. Part 1.
A first look at eigenvectors and eigenvalues. Definition, quick examples, and a theorem. More on this in part 2!Video. Notes.
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.
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.