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The Grothendieck inequality asserts the existence of an universal constant K with the property:
If A is an n by n matrix with | \sum_{i,j=1}^n a_{i j} s_i t_j | is less or equal to 1 for all vectors
s, t with |s_i|, |t_i| less or equal to 1, then | \sum_{i,j}^n a_{i j} | less or equal to K(n).
for any choice of unit vectors x_1,..., x_n; y_1,...,y_n of a Hilbert space H, The limit of K(n)
remains finite as n → ∞ and is the universal constant K of Grothendieck. We will discuss this inequality along with many of its surprising consequences. |