
\begin{abstract}
In this paper I define the Householder transformation, then put it to work in
several ways:

\begin{itemize}
\item To illustrate the usefulness of geometry to elegantly derive and prove
seemingly algebraic properties of the transform;

\item To demonstrate an application to numerical linear algebra ---
specifically, for matrix determinants and inverses;

\item To show how geometric notions of determinant and matrix norm can be used
to easily understand round-off error in Householder and Gaussian-elimination
methods.
\end{itemize}

These are notes to accompany a talk given to graduate students in mathematics.
However, most of the content (except references to the orthogonal group) should
be accessible to an undergraduate with a course in introductory linear algebra.

\end{abstract}
