Math 2406: Abstract Vector Spaces

Lecture 27 Plan  (Tuesday, December 4, 2007).

Apostol 7.12, 7.13, 7.15, 7.19.

There are two main topics for today:
1. Conic sections
. We'll use eigenvalues to determine whether a quadratic equation represents an ellipse, a hyperbola, a parabola, or a degenerate case.
2. Unitary transformations. Unitary transformations have some of the nice properties of Hermitian transformations, one of the most important being that a unitary transformation has an orthonormal eigenbasis.