Matrix norms, sup,max and headache I am reading (again) about
matrix norms and have a few questions. The definition I have
says that given any norm on the space of -dimensional vectors
with real entries, the subordinate matrix norm on the space of
matrices with real entries is defined by I've also read that it
can be defined as, The way I "understand" the second definition
is that we take all the vectors whose norm is one, and multiply
them with the matrix A to create a set of vectors, say, I
believe that there is an infinite number of vectors with norm
one.. We then take the norm of all these new vectors to get a
set of real numbers. We now find the smallest real number that
is larger than all the real numbers in this set, and use it as
the norm of the matrix . By the definition of , I believe that
this number that is larger than all numbers in our set is not
part of the set. As for the first definition, I am tempted to
say that we take all vectors and divide then by to make a unit
vector.We then multiply th