The Complex Plank Problem, Revisited

Abstract Ball’s complex plank theorem states that if $$v_1,\dots ,v_n$$ v 1 , ⋯ n are unit vectors in $${\mathbb {C}}^d$$ C d , and $$t_1,\dots ,t_n$$ t non-negative numbers satisfying $$\sum _{k=1}^nt_k^2 = 1$$ ∑ k = 2 then there exists a vector v for which $$|\langle v_k,v \rangle | \ge t_k$$ | ⟨ ⟩ ≥ every k . Here we present streamlined version of original proof.