What do you mean by "split"?
I am trying to prove that the charactertic polynomial of a diagonalizable matrix will "split".
I know intuitively this has to be true because a diagonalizable matrix would be similar to a diagonal one, which would have the same charactristic polynomial... and obviously that polynomial will split since its determinant will just be determined by the diagonal entries.. but I am stuck on how to formally prove it.
Thank you in advance for any tips!!!