minimal polynomial
A "minimal polynomial" is crucial in linear algebra and field theory, representing the simplest polynomial that nullifies a matrix or algebraic element.
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Definition
C2Linear Algebra
(technical, academic)The simplest polynomial of a matrix that, when applied to the matrix, results in the zero matrix.
Example
- To find the minimal polynomial of the matrix, we need to determine the lowest-degree polynomial that nullifies it.
C2Field Theory
(technical, academic)The simplest polynomial for which a given algebraic element in an extension field is a root.
Example
- The minimal polynomial of the element α over the field K is the polynomial of smallest degree with α as a root.
Similar
Terms that have similar or relatively close meanings to "minimal polynomial":
primitive polynomialcharacteristic polynomialprimitive elementpolynomial basis