Let 
be a vector
norm of a vector 
such that
 |
Then 
is a matrix
norm which is said to be the natural norm induced (or subordinate) to the vector norm 
. For any natural norm,
 |
where 
is the identity matrix. The natural matrix norms
induced by the L1-norm, L2-norm,
and L-infty-norm are called the maximum
absolute column sum norm, spectral norm, and
maximum absolute row sum norm, respectively.
