relation between minimal polynomial and jordan normal form

Question

I just solved some exercises on minimal polynomials and i remember that there is a relation between the minimal polynomial and the jordan normal form.

But my question is the following : knowing the minimal polynomial of a given matrix $A$ what information can we get about the jordan normal form (without computing it).

Thanks in advance!

Answer 1

The multiplicity of an eigenvalue in the minimal polynomial is the size of that eigenvalue's largest Jordan block. See the "Complex matrices" topic in Wikipedia article "Jordan normal form."