- #1
phosgene
- 146
- 1
Homework Statement
Let C =
2,0,-2
1,1,2
-1,-1,-1
Use the Cayley-Hamilton theorem to compute C^3.
Homework Equations
Cayley-Hamilton theorem says that every square matrix satisfies its own characteristic equation.
[itex]C^3=PD^3P^{-1}[/itex]
where P is the matrix formed from linearly independant eigenvectors of C and D is the diagonal matrix formed from the eigenvalues of C.
The Attempt at a Solution
I get the characteristic equation of C is
[itex]\lambda^3 - 2\lambda^2 - \lambda - 2 = 0 [/itex]
I get stuck because I can't factorise this and get the eigenvalues to proceed. Is there some trick to factorising cubics like this?