A typical first course on linear algebra is usually restricted to vector spaces over the real numbers and the usual positive-definite inner product. Hence, the proof that dim(S) + dim(S ⊥) = dim(V) is not presented in a way that generalizes to non-positive?definite inner products or to vector spaces over other fields. In this note we give such a proof.
ASJC Scopus subject areas
- General Mathematics