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- Jordan_normal_form abstract "In linear algebra, a Jordan normal form (often called Jordan canonical form)of a linear operator on a finite-dimensional vector space is an upper triangular matrix of a particular form called a Jordan matrix, representing the operator with respect to some basis. The form is characterized by the condition that any non-diagonal entries that are non-zero must be equal to 1, be immediately above the main diagonal (on the superdiagonal), and have identical diagonal entries to the left and below them. If the vector space is over a field K, then a basis with respect to which the matrix has the required form exists if and only if all eigenvalues of M lie in K, or equivalently if the characteristic polynomial of the operator splits into linear factors over K. This condition is always satisfied if K is the field of complex numbers. The diagonal entries of the normal form are the eigenvalues of the operator, with the number of times each one occurs being given by its algebraic multiplicity.If the operator is originally given by a square matrix M, then its Jordan normal form is also called the Jordan normal form of M. Any square matrix has a Jordan normal form if the field of coefficients is extended to one containing all the eigenvalues of the matrix. In spite of its name, the normal form for a given M is not entirely unique, as it is a block diagonal matrix formed of Jordan blocks, the order of which is not fixed; it is conventional to group blocks for the same eigenvalue together, but no ordering is imposed among the eigenvalues, nor among the blocks for a given eigenvalue, although the latter could for instance be ordered by weakly decreasing size. The Jordan–Chevalley decomposition is particularly simple with respect to a basis for which the operator takes its Jordan normal form. The diagonal form for diagonalizable matrices, for instance normal matrices, is a special case of the Jordan normal form. The Jordan normal form is named after Camille Jordan.".
- Jordan_normal_form thumbnail Jordan_blocks.svg?width=300.
- Jordan_normal_form wikiPageExternalLink JordanCanonicalForm.html.
- Jordan_normal_form wikiPageID "312877".
- Jordan_normal_form wikiPageRevisionID "600472343".
- Jordan_normal_form hasPhotoCollection Jordan_normal_form.
- Jordan_normal_form subject Category:Linear_algebra.
- Jordan_normal_form subject Category:Matrix_decompositions.
- Jordan_normal_form subject Category:Matrix_normal_forms.
- Jordan_normal_form subject Category:Matrix_theory.
- Jordan_normal_form type Abstraction100002137.
- Jordan_normal_form type Algebra106012726.
- Jordan_normal_form type Cognition100023271.
- Jordan_normal_form type Content105809192.
- Jordan_normal_form type Decomposition106013471.
- Jordan_normal_form type Discipline105996646.
- Jordan_normal_form type Form106290637.
- Jordan_normal_form type KnowledgeDomain105999266.
- Jordan_normal_form type LanguageUnit106284225.
- Jordan_normal_form type Mathematics106000644.
- Jordan_normal_form type MatrixDecompositions.
- Jordan_normal_form type MatrixNormalForms.
- Jordan_normal_form type Part113809207.
- Jordan_normal_form type PsychologicalFeature100023100.
- Jordan_normal_form type PureMathematics106003682.
- Jordan_normal_form type Relation100031921.
- Jordan_normal_form type Science105999797.
- Jordan_normal_form type VectorAlgebra106013298.
- Jordan_normal_form type Word106286395.
- Jordan_normal_form comment "In linear algebra, a Jordan normal form (often called Jordan canonical form)of a linear operator on a finite-dimensional vector space is an upper triangular matrix of a particular form called a Jordan matrix, representing the operator with respect to some basis.".
- Jordan_normal_form label "Forma canonica di Jordan".
- Jordan_normal_form label "Forma canónica de Jordan".
- Jordan_normal_form label "Forma canônica de Jordan".
- Jordan_normal_form label "Jordan normal form".
- Jordan_normal_form label "Jordan-normaalvorm".
- Jordan_normal_form label "Jordansche Normalform".
- Jordan_normal_form label "Postać Jordana".
- Jordan_normal_form label "Réduction de Jordan".
- Jordan_normal_form label "Жорданова матрица".
- Jordan_normal_form label "ジョルダン標準形".
- Jordan_normal_form label "若尔当标准型".
- Jordan_normal_form sameAs Jordanova_normální_forma.
- Jordan_normal_form sameAs Jordansche_Normalform.
- Jordan_normal_form sameAs Forma_canónica_de_Jordan.
- Jordan_normal_form sameAs Réduction_de_Jordan.
- Jordan_normal_form sameAs Forma_canonica_di_Jordan.
- Jordan_normal_form sameAs ジョルダン標準形.
- Jordan_normal_form sameAs 조르당_표준형.
- Jordan_normal_form sameAs Jordan-normaalvorm.
- Jordan_normal_form sameAs Postać_Jordana.
- Jordan_normal_form sameAs Forma_canônica_de_Jordan.
- Jordan_normal_form sameAs m.01tf90.
- Jordan_normal_form sameAs Q838495.
- Jordan_normal_form sameAs Q838495.
- Jordan_normal_form sameAs Jordan_normal_form.
- Jordan_normal_form wasDerivedFrom Jordan_normal_form?oldid=600472343.
- Jordan_normal_form depiction Jordan_blocks.svg.
- Jordan_normal_form isPrimaryTopicOf Jordan_normal_form.
