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.