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!


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."

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