You are here

An Elementary Treatment of General Inner Products

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 Spaces
Applicable Course(s): 3.8 Linear/Matrix Algebra

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 \(\dim(\mathcal{S}) + \dim(\mathcal{S^\perp}) = \dim(\mathcal{V})\) 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
Average: 4 (2 votes)