The Complex Plank Problem, Revisited.

Ball's complex plank theorem states that if v 1 , ⋯ , v n are unit vectors in  C d , and t 1 , ⋯ , t n are non-negative numbers satisfying ∑ k = 1 n t k 2 = 1 , then there exists a unit vector v in C d for which | ⟨ v k , v ⟩ | ≥ t k for every  k . Here we present a streamlined version of Ball's original proof.