Column bounded matrices and Grothendieck's inequalities
Abstract
It follows from Grothendieck's little inequality that to any complex (m x n) matrix X of column norm at most 1, and an 0 <e <1, there exist a natural number q, an (m x q) matrix C with (1-e)2 ≤ CC* ≤ (4/π) (1 + e)2 and an (q x n ) matrix Z with entries in the complex torus such that X= q-(1/2)(CZ). Both of Grothendieck's complex inequalities follow from this factorization result.
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