Annihilating space

In mathematics, the annihilator or annihilating space (or sometimes polar space) X_annihilator of a subspace X of a vector space S with a bilinear operator b, is defined by

$X_{\mathrm{annihilator}} := \{ s \in S | \forall_{x \in X} b(s, x) = 0 \}.$

If the bilinear operator is a metric tensor, then the annihilating space is called the orthogonal complement.