Definition talk:Minimal Polynomial

In the part "Also see", that theorems that are supposed to be proved are part of the definition. I'm not an expert in this area of mathematics, but I think the definition can be weakened. --Dan232 02:15, 23 August 2011 (CDT)

Minimal

Should it not be part of the definition that $\mu \left(x\right)$ is of least possible degree? -- TheSpleen (talk) 11:54, 11 September 2013 (UTC)

No, for this follows from the "irreducible" property. But I agree that the definition you propose should be documented, as it is used on Minimal Polynomial is Irreducible. We could also algebraically define it as the unique generator of the ideal $\operatorname{Ann}(\alpha)$ of polynomials $p$ with $p(\alpha)=0$ (since polynomial rings in one variable are PIDs); all three are equivalent. — Lord_Farin (talk) 15:22, 11 September 2013 (UTC)

Disambiguation

This page is about field theory, but there is another (but somewhat similar) meaning in linear algebra. Results about this definition include Existence of Minimal Polynomial for Square Matrix over Field. Is there anyone to organize the pages? --Fake Proof (talk) 13:18, 21 July 2021 (UTC)