* Power Method
v_{k+1} = A v_k, k = 0,1,2

** Properties
1. \frac{A v_k}{||v_k||} \rightarrow v_1
2. \frac{v_k^T A v_k}{v_k^T v_k} \rightarrow \lambda_1
3. If \lambda is a n eigenvalue of A, then \frac{1}{\lambda} is an eigenvalue of A^-1
4. Av = \lambda v
   Av - \mu v = (\lambda-\mu)v = (A - \mu I)v
5. If \lambda is an eigenvalue of A, then \lambda - \mu is an eigenvalue of A \cdot \mu I

** Shifting Eigenvalues
1. Partition [\lambda_n, \lambda_1]


* Lanczos Algorithm

#+BEGIN_SRC c
  for (int i = 0; i < n; i++) {
    sum = a0;
    v_dot_v(a[i], x);

    b[i] = sum;
  }
#+END_SRC