Given a diagonalizable square matrix A with characteristic polynomial $c(x) = (x{^2}-4)^{600}(x^2-1)^{800}$, determine the minimal polynomial.
This is a practice question I was given. Based on examples and things I've read, I think the min poly would be $m(x)= (x^2-4)(x^2-1)$, however I cannot find information on how diagonalizability affects the min poly.
Can someone please tag helpful articles or explain, and confirm the correct answer?
Yes, your answer is correct. The matrix $A$ is similar to a diagonal matrix $D$ which has no other entries in the main diagonal than $1$, $-1$, $2$, and $-2$. Therefore, its minimal polynomial (which is the minimal polynomial of $D$) is the one that you mentioned.