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