Examples of 'minimal polynomial' in a sentence
Meaning of "minimal polynomial"
minimal polynomial: In mathematics, the minimal polynomial of a matrix or an algebraic element is the monic polynomial with the smallest degree that has the element as a root. It is an important concept in algebra and linear algebra, used to understand the properties and relationships of matrices and algebraic elements
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- 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.
- 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.
How to use "minimal polynomial" in a sentence
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minimal polynomial
This polynomial is called its minimal polynomial.
The minimal polynomial of a primitive element is a primitive polynomial.
Are just the roots of the minimal polynomial.
The minimal polynomial divides the characteristic polynomial.
Extension field minimal polynomial.
A minimal polynomial is irreducible.
Therefore the degree of the minimal polynomial is the sum of all indices.
The minimal polynomial is thus defined to be the monic polynomial which generates IT.
The characteristic polynomial and minimal polynomial have the same irreducible factors.
Minimal polynomial of a matrix and linear operator ; nth power of matrix.
Show the characteristic and minimal polynomial of C are the same and both equal q.
Minimal polynomial ( field theory ).
For any positive integer, let be the minimal polynomial of over.
Prove that the minimal polynomial of T has no repeated roots.
The characteristic polynomial is formula 3, which is a multiple of the minimal polynomial by a factor formula 4.
See also
If the minimal polynomial of α exists, it is unique.
More precisely, it equals the degree of the minimal polynomial having α as a root.
Let V be a finite-dimensional vector space over a field k and f, V → V { \ displaystyle f, V \ to V } a linear map with minimal polynomial q.
This follows because its minimal polynomial over the rationals has degree 3.
The characteristic polynomial as well as the minimal polynomial of C ( p ) are equal to pp.
This follows since the minimal polynomial is separable, because the roots of unity are distinct.
Let Mi ( x ) be the minimal polynomial of αi, then.
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Examples of using Minimal
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The following minimal dimensions shall be met
