## Grothendieck's Constant

Let A be an Real Square Matrix and let and be real numbers with . Then Grothendieck showed that there exists a constant independent of both A and satisfying

 (1)

in which the vectors and have a norm in any Hilbert Space. The Grothendieck constant is the smallest Real Number for which this inequality has been proven. Krivine (1977) showed that
 (2)

and has postulated that
 (3)

It is related to Khintchine's Constant.

References

Krivine, J. L. Sur la constante de Grothendieck.'' C. R. A. S. 284, 8, 1977.

Le Lionnais, F. Les nombres remarquables. Paris: Hermann, p. 42, 1983.