We have the Euclidean norm (or ) for a vector on the vector space ; .
Given a vector norm on the induced matrix norm for m x m matrices A is defined by
That is , is the smallest number such that
So given the Euclidian-norm for a vector the induced matrix norm
Can anyone proof/explain why?
In my book it is given but I donīt see it directly, i think it has something to do with the fact that is symmetric.