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- Frobenius_normal_form abstract "In linear algebra, the Frobenius normal form or rational canonical form of a square matrix A with entries in a field F is a canonical form for matrices obtained by conjugation by invertible matrices over F. The form reflects a minimal decomposition of the vector space into subspaces that are cyclic for A (i.e., spanned by some vector and its repeated images under A). Since only one normal form can be reached from a given matrix (whence the "canonical"), a matrix B is similar to A if and only if it has the same rational canonical form as A. Since this form can be found without any operations that might change when extending the field F (whence the "rational"), notably without factoring polynomials, this shows that whether two matrices are similar does not change upon field extensions. The form is named after German mathematician Ferdinand Georg Frobenius.Some authors use the term rational canonical form for a somewhat different form that is more properly called the primary rational canonical form. Instead of decomposing into a minimal number of cyclic subspaces, the primary form decomposes into a maximal number of cyclic subspaces. It is also defined over F, but has somewhat different properties: finding the form requires factorization of polynomials, and as a consequence the primary rational canonical form may change when the same matrix is considered over an extension field of F. This article mainly deals with the form that does not require factorization, and explicitly mentions "primary" when the form using factorization is meant.".
- Frobenius_normal_form wikiPageExternalLink RationalCanonicalForm.html.
- Frobenius_normal_form wikiPageExternalLink ft_gateway.cfm?id=281570&type=pdf.
- Frobenius_normal_form wikiPageExternalLink abs_storjohann.html.
- Frobenius_normal_form wikiPageExternalLink canonical.pdf.
- Frobenius_normal_form wikiPageID "1087818".
- Frobenius_normal_form wikiPageRevisionID "597680222".
- Frobenius_normal_form hasPhotoCollection Frobenius_normal_form.
- Frobenius_normal_form subject Category:Linear_algebra.
- Frobenius_normal_form subject Category:Matrix_normal_forms.
- Frobenius_normal_form type Abstraction100002137.
- Frobenius_normal_form type Form106290637.
- Frobenius_normal_form type LanguageUnit106284225.
- Frobenius_normal_form type MatrixNormalForms.
- Frobenius_normal_form type Part113809207.
- Frobenius_normal_form type Relation100031921.
- Frobenius_normal_form type Word106286395.
- Frobenius_normal_form comment "In linear algebra, the Frobenius normal form or rational canonical form of a square matrix A with entries in a field F is a canonical form for matrices obtained by conjugation by invertible matrices over F. The form reflects a minimal decomposition of the vector space into subspaces that are cyclic for A (i.e., spanned by some vector and its repeated images under A).".
- Frobenius_normal_form label "Frobenius normal form".
- Frobenius_normal_form label "Frobenius-Normalform".
- Frobenius_normal_form label "Invariants de similitude".
- Frobenius_normal_form label "Фробениусова нормальная форма".
- Frobenius_normal_form sameAs Frobenius-Normalform.
- Frobenius_normal_form sameAs Invariants_de_similitude.
- Frobenius_normal_form sameAs m.044w_d.
- Frobenius_normal_form sameAs Q1469423.
- Frobenius_normal_form sameAs Q1469423.
- Frobenius_normal_form sameAs Frobenius_normal_form.
- Frobenius_normal_form wasDerivedFrom Frobenius_normal_form?oldid=597680222.
- Frobenius_normal_form isPrimaryTopicOf Frobenius_normal_form.