Math 42 Homework
h
- assignment 1
** due Thurs 9/28 **

Ch 0: 1, 5, 8

Ch 1: 3, 4, 6

Also: Prove that every centrally symmetric compact set,

with nonempty
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

coordinates.")

assignment 3: ** due Dec 12 **
click here