Outline of the proof

Friday 15th of April, 2005 in Uni

General proof of the spectral theorem.

Two steps.

  1. Show that there is a real eigenvalue for T.
  2. By iteration and the theorem I already proved, show that there is an orthonormal basis composed entirely of eigenvectors of T.

Part 1.
Use the Fundamental Theorem of Algebra. Play with complex numbers to show that a linear map with the same matrix has a “real” eigenvalue.

Part 2.
Use induction, etc.

I think I’ll post a LaTeX’ed pdf of this when I’m finished. Maths sucks in plain text.