The Orthogonal Complement of a Linear Subspace is a Linear Subspace

Let $V$ together with $\langle\cdot,\cdot\rangle$ be a \reftext{def:complex-inner-product-space-2026a}{complex inner product space} and let $W$ be a \reftext{def:linear-subspace-2026a}{linear subspace} of $V$. Then the \reftext{def:orthogonal-complement-2026a}{orthogonal complement} $W^{\perp}$ is a linear subspace of $V$.