Orthogonal complement

In the mathematical fields of linear algebra and functional analysis, the orthogonal complement of a subspace ${\displaystyle W}$ of a vector space ${\displaystyle V}$ equipped with a bilinear form ${\displaystyle B}$ is the set ${\displaystyle W^{\perp }}$ of all vectors in ${\displaystyle V}$ that are orthogonal to every vector in ${\displaystyle W}$. Informally, it is called the perp, short for perpendicular complement. It is a subspace of ${\displaystyle V}$.