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We show that, for any rational p ∈ [1,∞) [p is an element of the set [1, infinity)]  except p = 1, 2, unless P = NP, there is nopolynomial time algorithm which approximates the matrix p-norm to arbitrary relative precision. Wealso show that, for any rational p ∈ [1,∞) [p is an element of the set [1, infinity)] including p = 1, 2, unless P = NP, there is no polynomialtimealgorithm which approximates the ∞, p [infinity, p] mixed norm to some fixed relative precision.National Science Foundation (U.S.) (Grant ECCS-0701623

Matrix p-Norms Are NP-Hard to Approximate If $p\neq1,2,\infty$