A lower bound for the product of linear forms

Let x1 ,… xk be unit vectors in an n-dimensional unitary spacek ≤ n. Let A be the Gram matrix based on x1 ,… xk , i.e.A = [(xi xj )],i,j = 1,…,kThen where λ is the smallest eigenvalue of A. This inequality can be interpreted as a lower bound for the largest projection of the decomposable tensor on a completely symmetric power .