Definitions

• Condition number cond(A) = (max Wi)/(min Wi).

  • If cond(A) = , A is singular.
  • If cond(A) very large (106, 1012), A is ill-conditioned.

• Consider Ax = b. If A is singular, there is some subspace of x (the nullspace) such that Ax = 0.

• The nullity is the dimension of the nullspace.

• The subspace of b such that Ax = b is the range.

• The rank of A is the dimension of the range.

Notes: