1. floating point
   1. machine representation
      1. denormalized number
      2. normalized number
   2. distance
      1. absolute
      2. relateive?
      3. next larger fp
   3. exactly represented
   4. condition number for scalar substraction
      1. proof
   5. round off error
2. Norm calculation
   1. vector
      1. column
      2. row
      3. Triangle Inequality
      4. Hdder inequality
      5. Cauchy Schwartz inequality
   2. matrix
      1. def?
      2. 1-norm, inf-norm, 2-norm
      3. submultiplication inequality
      4. Inverse of Perturbed Identity !
         1. Inverse of Perturbed Matrix !
      5. distance to signularity
         1. absolute
         2. relative
3. Linear System
   1. Linear System error bound
      1. proof
   2. Direct method
      1. stability factor
   3. Matrix and RHS perturbation
4. Factorization
   1. LU Factorization
      1. Calculate L and U?
      2. LU with partial pivoting
         1. Calculate L, U, P?
      3. Permutation
   2. Cholesky factorization
      1. How to? P65
      2. HPD
         1. Hermitian
            1. def? P19
         2. Positive definate
            1. def?
   3. QR Factorization
      1. Givens rotation
         1. def?
      2. How to?
   4. SVD Factorization
      1. Unitary
         1. def?
      2. Orthogonal
         1. def?
      3. singular value
         1. singular value VS 2-norm
         2. singular value VS condition # P79
         3. singular value VS distance to singularity P79
5. Least Square
   1. Thin SVD(Reduced SVD)
   2. Column Space
      1. Basis of R(A) V.S. U
   3. Kernel Space
      1. Basis of Ker(A) V.S. V
   4. Moore-Penrose Inverse
      1. m<n
      2. m>n
   5. Minimal-norm LS solution
   6. RHS Perturbation
6. GMRES
   1. Diagonalizable / Factorization
      1. eigenvalue
   2. Krylov space
   3. minimal polynomial
      1. characterizing polynomial
   4. proof: GMRES ends in $n$ iteration
   5. GMRES bound