##  [Minimal Polynomial](/minimal-polynomial) 

  ##  [Minimal Polynomial](https://puremath.quantumdictionary.io/minimal-polynomial-0) 

  

 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The monic polynomial of least degree over the base ring or field that annihilates a given linear operator or algebraic element; i.e., the monic p of minimal degree with p(T)=0.

 

 

 

 

 





 

 



 ##  [Minimal Polynomial](https://algebra.quantumdictionary.io/minimal-polynomial-1) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The unique monic polynomial of least degree over the base field that annihilates a given algebraic element or linear operator; equivalently the generator of the principal ideal of annihilating polynomials.