Principles of Quantum Mechanics · Problem 1.4.1

Mathematical Introduction — R. Shankar

Physics — Quantum Mechanics · subspaces

Problem

In a space

\mathbb{V}^n

, prove that the set of all vectors

\{|V^1_\perp\rangle, |V^2_\perp\rangle, \ldots\}

, orthogonal to any

|V\rangle \neq 0

, form a subspace

\mathbb{V}^{n-1}