TITLE: Physical meaning of norm of a matrix
QUESTION [12 upvotes]: I know norm of a vector is a length of a vector from origin. So what is the motivation behind defining the norm of the matrix? What is the physical meaning of norm of a matrix?
Any help is appreciated.
Thanks.

REPLY [2 votes]: The picture is particularly simple if you consider a positive self-adjoint matrix. In this case the operator norm is the largest eigenvalue.  From the point of view of quantum mechanics, this is the largest possible outcome for the corresponding variable in any given experiment.