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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.