Home > Affine Geometry, Analysis, Geometry > IMC 2013 Problem 8

IMC 2013 Problem 8


Problem 8. Suppose that {v_1,..,v_d} are unit vectors in {\Bbb{R}^d}. Prove that there exists a unit vector {u} such that

\displaystyle |u\cdot v_i|\leq 1/\sqrt{d}

for {i=1,2,..,d}.

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