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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. Such matrix has each non-zero off-diagonal entry equal to 1, immediately above the main diagonal (on the superdiagonal), and with 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 the matrix 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 lec_notes_revised_at_the_end.pdf.
• Jordan_normal_form wikiPageExternalLink JordanCanonicalForm.html.
• Jordan_normal_form wikiPageExternalLink system_equations_solver.
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• Jordan_normal_form wikiPageRevisionID "679407922".
• Jordan_normal_form wikiPageWikiLink Academic_Press.
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• Jordan_normal_form wikiPageWikiLink Banach_space.
• Jordan_normal_form wikiPageWikiLink Basis_(linear_algebra).
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• Jordan_normal_form wikiPageWikiLink Cambridge_University_Press.
• Jordan_normal_form wikiPageWikiLink Camille_Jordan.
• Jordan_normal_form wikiPageWikiLink Canonical_basis.
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• Jordan_normal_form wikiPageWikiLink Category:Linear_algebra.
• Jordan_normal_form wikiPageWikiLink Category:Matrix_decompositions.
• Jordan_normal_form wikiPageWikiLink Category:Matrix_normal_forms.
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• Jordan_normal_form wikiPageWikiLink Pole_(complex_analysis).
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• Jordan_normal_form wikiPageWikiLink Ring_(mathematics).
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• Jordan_normal_form wikiPageWikiLink Similar_(linear_algebra).
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• Jordan_normal_form wikiPageWikiLink Splitting_field.
• Jordan_normal_form wikiPageWikiLink Springer_Science+Business_Media.
• Jordan_normal_form wikiPageWikiLink Square_matrix.
• Jordan_normal_form wikiPageWikiLink Structure_theorem_for_finitely_generated_modules_over_a_principal_ideal_domain.

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