# minimal polynomial

> English word · Noun

## Definitions
1. For a given square matrix M over some field K, the smallest-degree monic polynomial over K which, when applied to M, yields the zero matrix.
2. Given an algebraic element α of a given extension field of some field K, the monic polynomial of smallest degree of which α is a root.

## Source
Compiled from Wiktionary via kaikki.org (CC BY-SA). Data vintage: 2026-05-06.
Canonical page: https://plainspell.com/en/word/minimal-polynomial