Second Midterm material:

Section 2.1:
• Calculate vector and matrix norms: 1, 2, infinity, p, A, F
• Prove functions are norms, prove norm inequalities
• Use Cauchy-Schwarz inequality
Section 4.1:
• 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.)
Section 5.2:
• Know what eigenvalues and eigenvectors are, calculate them using the characteristic funciton.
• Why are iterative methods needed to find eigenvalues?
Section 5.3:
• 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.
Secion 8.3:
• Know the splitting matrices for the methods we discussed
• Calculate convergence properties for given matrices
Section 8.4-8.7:
• 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.