For the first part, the Cayley-Hamilton theorem states that a square matrix satisifies its characteristic equation.
The charpoly is
So, confirm that
I'm having trouble with a few of the harder linear algebra concepts from the eigenvalue chapter.
1) Using the matrix A= | 3 -2 |
| 1 2 |
verify the Cayley Hamilton theorem.
2) Given the rotation matrix Rtheta = | cos -sin|
| sin cos|
show the matrix has eigenvectors and eigenvalues corresponding to
lambda= e^i*theta : |1|
|-i|
lambda= e^-i*theta |1|
|i |
3)Show that similar matrices A and B have the same eigenvalues. Thus you must show that det(A-lambda*I)= det(B-lambda*I)
Thanks to anyone takes a look at this.