Week 7
When diagonalization fails: More on eigenvalues and eigenvectors, Jordan Canonical Form, inner products
7.1: Diagonalization and what can go wrong
While diagonalization is very useful, we will encounter cases where it is not possible, and how to be as close as possible.
In these notes, you’ll learn how to use the Jordan Canonical Form process when a square matrix is not diagonalizable, how to recognize when you need to, and why.
The concepts of inner products and orthonormal bases are central to understanding the geometry of vector spaces and their applications in linear algebra.
In these notes, you’ll explore the idea of an inner product, a generalization of the dot product, leading to the value of orthogonal bases, and how to find orthonormal bases using the Gram Schmidt process. Orthonormal bases have widespread applications in regression and many other computations we use every day.
7.2: Inner products and orthonormal bases
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 7 recitation slides and solutions!
Ryann Joseph 