The Householder Transformation, Swiss Army Knife of Numerical Linear Algebra In this talk I will define the Householder transformation, then immediately put it to work in several ways: * To illustrate the usefulness of geometry to elegantly derive and prove seemingly algebraic properties of the transform; * To demonstrate an underappreciated use of the Householder transform for numerical linear algebra -- specifically, for matrix determinants and inverses; * 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; * To prove that not only the applied grads can have fun with numerical techniques; and * To give an application of Householder transforms to dumb on-board processors, subtitled "What I did over the winter break while the rest of you were having a real vacation." John Kerl Graduate Student Colloquium January 25, 2007