by Jack E. Graver
This article originally appeared in:
College Mathematics Journal
January, 2011
Subject classification(s):
Algebra and Number Theory | Linear Algebra | Inner Product SpacesApplicable Course(s):
3.8 Linear/Matrix AlgebraA 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 \(\dim(\mathcal{S}) + \dim(\mathcal{S^\perp}) = \dim(\mathcal{V})\) is not presented in a way that generalizes to non-positive-definite inner products or to vector spaces over other fields. In this note the author gives such a proof.
A pdf copy of the article can be viewed by clicking below. Since the copy is a faithful reproduction of the actual journal pages, the article may not begin at the top of the first page.
To open this file please click here.
Capsule Course Topic(s):
Linear Algebra | Inner Product Spaces