How to proof this theorem?
Let $S$ be a subspace of $\mathbb{C}^n$ of dimension $k\geq 2$, and let $\mathbf{w}\neq \mathbf{0}$ be a vector in $\mathbb{C}^n$. Then there are at least $k-1$ linearly independent unit vectors in $S$ that are orthogonal to $\mathbf{w}$.
Thank you.