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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!

Git Gud
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sigmatau
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  • http://math.stackexchange.com/questions/82607/why-does-the-largest-jordan-block-determine-the-degree-for-that-factor-in-the-mi?rq=1 has some information. I'm not sure there's much more you can do. – Evan Aug 12 '13 at 16:08

1 Answers1

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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."

user0
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