Class 23

beginning of eigenvalues and eigenvectors for (square) matrices. (Section 6.1 and complex eigenvalues and eigenvectors in Section B.2)
Problems:
- What are the eigenvalues and eigenvectors of a projection matrix P (i.e. a matrix such that P²=P)? Why?
- What are the eigenvalues of a 2 by 2 reflection matrix? Why?
- What are the eigenvalues of a 2 by 2 rotation matrix? Why?
- What are the eigenvalues of a unitary matrix? Why?
- How are the eigenvalues of A and A² related? Why?
- How are the eigenvalues of AB and BA related? Why?
- If you are given an eigenvalue of A, how can you find the corresponding eigenvector?
  If you are given an eigenvector of A, how can you find the corresponding eigenvalue?
- Problems 12 and 13 page 363 of the text.