Math 42 Homework
assignment 3: due Dec 12
- assignment 1 due Thurs 9/28
Ch 0: 1, 5, 8
Ch 1: 3, 4, 6
Also: Prove that every centrally symmetric compact set,
interior, is contained
in a unique centrally symmetric ellipsoid
of minimal volume.
(This is called the John ellipsoid.)
Also: Let N be a norm on a finite dimensional real vector space.
Prove that the unit ball of N is an ellipsoid if and only if
N is the diagonal part of an inner product.
- assignment 2 due Thursday Oct 19
Ch 2. 5,8
Ch 3. 1,3
Also: The Heisenberg group is the group of
upper triangular 3x3 matrices with 1s
on the diagonal. Put a left-invariant metric
on the Heisenberg group and compute at least
one nontrivial geodesic. (Here nontrivial
means "not a straight line in the obvious