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**Arita** 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