I'm just learning a bit about the "minimal polynomial" today but there was a section from the book which I didn't understand. This is the section, and i've circled the bit i'm having trouble with.(adsbygoogle = window.adsbygoogle || []).push({});

http://img15.imageshack.us/img15/1825/97503873.jpg [Broken] (sorry, it won't let me post an image for some reason??)

Firstly it's a bit unclear to me what they mean by p(T)(v). Would this mean that you take the linear transformation T (or equivalently its matrix), stick it in the polynomial p to obtain a new linear transformation p(T), then perform this transformation on v?

Okay, assuming that's correct I can understand that p(T)=0 <=> p(T)(v)=0. But then how does this imply that the minimal polynomial is the least common multiple of all those other ones?! They say it like it's completely obvious!

Thanks.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# The minimal polynomial

Loading...

**Physics Forums | Science Articles, Homework Help, Discussion**