Class 21

Eigenvalues/Eigenvectors continued ...

• proof that eigenvalues do not change under a similarity transformation (though eigenvectors can change)
• Example of diagonalization of an operator L on polynomials V=P_2(R) in order to find L¹⁰(p(x)).
• further examples of finding eigenvalues of simple matrices
• proof of the two useful properties:
  • trace A = sum of the eigenvalues (including multiplicities)
  • det(A) = product of the eigenvalues (including multiplicities)