We have the Euclidean norm (or ) for a vector on the vector space ; . Given this vector norm on the induced matrix norm is; . Let be orthogonal ( I want to show that 1) for all and 2) that for any
.
Thanks a lot,
I have one more question about this norm;
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 as written in the first question why is the induced matrix norm
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.