Class 11

Eigenpairs and Linear Transformations; Complex Eigenpairs

1. First
   • --- two properties (and proofs in the diagonalizable case)! sum of eigenvalues is the trace; product of eigenvalues is the determinant
   • Finding the Fibonacci numbers using x_{k+1}=A x_k and eigenpairs; see the matlab file
2. Examples of finding eigenpairs and illustrating Theorem 7 in the text. Outline of proof of Theorem 7, page 324.
3. Matrix Representations of Linear functionals, i.e. L:V--> W, with respect to given bases beta in V and gamma in W.