Some norm stuff
October 1st, 2007 ~ Posted in: MathematicsNote that the unit ball of a norm satisfies the following properties: it is symmetric about the origin, convex, closed, bounded, and has a nonempty interior. Now show that any set with these properties is the unit ball of some norm (come up with an exact formula).
If
is a positive definite symmetric matrix, then define the quadratic norm
. Show that any norm on
is equivalent to some quadratic norm, with constants 1 and
:

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