Week 6
The foundations of linear algebra: Eigenvalues and eigenvectors, diagonalization
6.1: Linear transformations from V to W versus linear transformations from V to V
There is a large distinction between linear transformations going to a different vector space versus to the same vector space.
In these notes, you’ll explore the differences and similarities between linear transformations that map vectors from V to W, and those that map vectors from V to V.
Mapping from V to V gives us eigenvalues and eigenvectors, which permit more powerful linear transformations.
In these notes, you’ll learn we can pick vectors, eigenvectors, when a linear transformation is applied to them, only change in scale, by an eigenvalue, and not in direction. We can use this knowledge to diagonalize square matrices, which has broad applications in linear algebra.
6.2: Eigenvalues and eigenvectors
Recitation Slides
Attend recitation! But in case you were staying up late the night before or you’re looking to last-minute study cram, here are Week 6 recitation slides and solutions!
Ryann Joseph 