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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 wikiPageLength "15875".
- Frobenius_normal_form wikiPageOutDegree "38".
- Frobenius_normal_form wikiPageRevisionID "648611773".
- Frobenius_normal_form wikiPageWikiLink Basis_(linear_algebra).
- Frobenius_normal_form wikiPageWikiLink Block_matrix.
- Frobenius_normal_form wikiPageWikiLink Canonical_form.
- Frobenius_normal_form wikiPageWikiLink Category:Linear_algebra.
- Frobenius_normal_form wikiPageWikiLink Category:Matrix_normal_forms.
- Frobenius_normal_form wikiPageWikiLink Cayley–Hamilton_theorem.
- Frobenius_normal_form wikiPageWikiLink Characteristic_polynomial.
- Frobenius_normal_form wikiPageWikiLink Chinese_remainder_theorem.
- Frobenius_normal_form wikiPageWikiLink Companion_matrix.
- Frobenius_normal_form wikiPageWikiLink Diagonal_matrix.
- Frobenius_normal_form wikiPageWikiLink Dimension_(vector_space).
- Frobenius_normal_form wikiPageWikiLink Eigenvalue.
- Frobenius_normal_form wikiPageWikiLink Eigenvalues_and_eigenvectors.
- Frobenius_normal_form wikiPageWikiLink Elementary_divisors.
- Frobenius_normal_form wikiPageWikiLink Ferdinand_Georg_Frobenius.
- Frobenius_normal_form wikiPageWikiLink Field_(mathematics).
- Frobenius_normal_form wikiPageWikiLink Field_extension.
- Frobenius_normal_form wikiPageWikiLink Free_module.
- Frobenius_normal_form wikiPageWikiLink Hamel_basis.
- Frobenius_normal_form wikiPageWikiLink Hamel_dimension.
- Frobenius_normal_form wikiPageWikiLink Invariant_factor.
- Frobenius_normal_form wikiPageWikiLink Invariant_factors.
- Frobenius_normal_form wikiPageWikiLink Jordan_block.
- Frobenius_normal_form wikiPageWikiLink Jordan_matrix.
- Frobenius_normal_form wikiPageWikiLink Jordan_normal_form.
- Frobenius_normal_form wikiPageWikiLink Linear_algebra.
- Frobenius_normal_form wikiPageWikiLink Matrix_(mathematics).
- Frobenius_normal_form wikiPageWikiLink Matrix_similarity.
- Frobenius_normal_form wikiPageWikiLink Minimal_polynomial_(linear_algebra).
- Frobenius_normal_form wikiPageWikiLink Module_(mathematics).
- Frobenius_normal_form wikiPageWikiLink Monic_polynomial.
- Frobenius_normal_form wikiPageWikiLink Similar_(linear_algebra).
- Frobenius_normal_form wikiPageWikiLink Smith_normal_form.
- Frobenius_normal_form wikiPageWikiLink Square_matrix.
- Frobenius_normal_form wikiPageWikiLink Structure_theorem_for_finitely_generated_modules_over_a_principal_ideal_domain.
- Frobenius_normal_form wikiPageWikiLink Unit_(ring_theory).
- Frobenius_normal_form wikiPageWikiLink Vector_space.
- Frobenius_normal_form wikiPageWikiLinkText "Frobenius normal form".
- Frobenius_normal_form wikiPageWikiLinkText "Frobenius normal form#A rational normal form generalizing the Jordan normal form".
- Frobenius_normal_form wikiPageWikiLinkText "rational canonical form".
- Frobenius_normal_form hasPhotoCollection Frobenius_normal_form.
- Frobenius_normal_form wikiPageUsesTemplate Template:Ill.
- Frobenius_normal_form wikiPageUsesTemplate Template:Math.
- Frobenius_normal_form wikiPageUsesTemplate Template:Reflist.
- Frobenius_normal_form subject Category:Linear_algebra.
- Frobenius_normal_form subject Category:Matrix_normal_forms.
- Frobenius_normal_form hypernym Form.
- 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 sameAs Forma_normal_de_Frobenius.
- Frobenius_normal_form sameAs Frobenius-Normalform.
- Frobenius_normal_form sameAs Décomposition_de_Frobenius.
- Frobenius_normal_form sameAs צורה_רציונלית.
- Frobenius_normal_form sameAs m.044w_d.
- Frobenius_normal_form sameAs Фробениусова_нормальная_форма.
- Frobenius_normal_form sameAs Фробеніусова_нормальна_форма.
- Frobenius_normal_form sameAs Q1469423.
- Frobenius_normal_form sameAs Q1469423.
- Frobenius_normal_form wasDerivedFrom Frobenius_normal_form?oldid=648611773.
- Frobenius_normal_form isPrimaryTopicOf Frobenius_normal_form.