Linear Algebra

1. Norms
   1. notation
   2. 3 basic properties
   3. p-norms
   4. unit balls
   5. matrix norm (induced), geometric interpretation
2. Condition number (C)
   1. “physical” meaning
   2. In terms of relative errors?
   3. Magnitude of C effect on roundoff
3. Matrix multiplication
   1. two representations
   2. basic identities
4. Definitions
   1. range, rank, basis, inner product, linearly dependent/independent, singular
5. $Ax=b$ in terms of basis
   1. interpretation/basis of x, b
6. Eigenvalue decomposition
   1. Geometry of eigenvectors
   2. Why is the eigenvectors decomposition useful
   3. Show how to do it