Class 8

Eigenvectors and Eigenvalues/Chapter 5 cont... ( summary eigs. sec 5.1-.6)

• definitions for characteristic polynomial and equation
• finding roots of characteristic equation to find eigenvalues
• Theorem (AND proof): A is invertible iff 0 is NOT an eigenvalue
• definitions: algebraic multiplicity of eigenvalues
  similarity of two matrices
  Theorem (proof still to do): A similar to B implies that they both have the same characteristic polynomial and so the same eigenvalues with the same algebraic multiplicities.
• for next time: finish the proof and do Migration example - Markov matrix - equilibrium - proof of convergence - matlab file showing convergence; additional simple example on searching the web and rankings.