Orthogonal Complement of 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 $V$.

The \textbf{orthogonal complement} of $W$ is the set

where $0$ is the zero element of the field of \reftext{def:complex-numbers-2026a}{complex numbers}.