  We show that for any rational p \in [1,\infty) except p = 1, 2, unless P =
NP, there is no polynomial-time algorithm for approximating the matrix p-norm
to arbitrary relative precision. We also show that for any rational p\in
[1,\infty) including p = 1, 2, unless P = NP, there is no polynomial-time
algorithm approximates the \infty, p mixed norm to some fixed relative
precision.
