The linear polarization constant of Rn.

He present work deals with estimations of the n-th linear polarization constant c(H)n of an n-dimensional real Hilbert space H. We provide some new lower bounds on the value of sup║y║=1 │〈x1,y〉...〈xn,y〉, where x1, ... , xn are unit vectors in H. In particular, the results improve an earlier estimate of Marcus. However, the intriguing conjecture c(H) n= nn/2 remains open. [ABSTRACT FROM AUTHOR]