A is a square matrix and from its characteristic polynomial I am to figure out if is diagonalizable over all real numbers, not diagonalizable over all real numbers or if it's impossible to say.
x = lambda
f(x)= (x-3)^2 (x-5)
I know that the eigenvalues are 3 (with multiplicity 2) and 5 (with multiplicity 1)
I'm not sure what to do from here.
Another example is f(x)= (x^2-1)(x^2-2)
With this one i assume that there are no eigenvalues in the lR of A, so A would not be diagonalizable, but im not sure if it is correct