TOPICS
Search

Minimal Polynomial


A minimal polynomial is a smallest polynomial that can be used to represent a mathematical object.

For example, an algebraic number minimal polynomial gives a smallest polynomial of which a given number is a root, so x^2-x-1 is an algebraic number minimal polynomial of the golden ratio phi (as well as the the golden ratio conjugate -phi^(-1)) since, via the quadratic equation, the roots of x^2-x-1 are

 x=1/2(1+/-sqrt(5),).

See also

Algebraic Number Minimal Polynomial, Extension Field Minimal Polynomial, Matrix Minimal Polynomial

Explore with Wolfram|Alpha

Cite this as:

Weisstein, Eric W. "Minimal Polynomial." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MinimalPolynomial.html

Subject classifications