MATRIX p-NORMS ARE NP-HARD TO APPROXIMATE IF p not equal 1, 2, infinity

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