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arXiv · 2505.04545

Column bounded matrices and Grothendieck's inequalities

Erik Christensen
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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 $(1-e)^2 \leq CC^* \leq (4/\pi) (1 + e)^2$ 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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Erik Christensen. 2025-05-07. Column bounded matrices and Grothendieck's inequalities. https://arxiv.org/abs/2505.04545

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