A second look at the matrix of the discrete Fourier transform. Proof that it is unitary. How to apply it to a function, and why it costs O(NlogN) vs O(N^2).
Review of some properties of unitary matrices. Orthogonality and completeness. A first look at the matrix of the discrete Fourier transform. Diagonalization and efficiency.
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.
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.
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.
