Second Midterm material:
- Calculate vector and matrix norms: 1, 2, infinity, p, A, F
- Prove functions are norms, prove norm inequalities
- Use Cauchy-Schwarz inequality
- The only thing you need to know for the test is why the 2-norm of a matrix is the first singular value. (See Theorem 4.2.1 in the book.)
- Know what eigenvalues and eigenvectors are, calculate them using the characteristic funciton.
- Why are iterative methods needed to find eigenvalues?
- Power method: How to do it, why to do it, why it works, why and when it converges, what it converges to, etc.
- Similar for inverse iteration and shift-and-invert strategies.
- Know the splitting matrices for the methods we discussed
- Calculate convergence properties for given matrices
- Be able to describe in words (and pictures) the idea of descent methods, including steepest (gradient) descent and conjugate gradient descent methods.
- I don't expect you to be able to calculate these.