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dc.contributor.authorPąk, Karol-
dc.date.accessioned2026-09-21T13:12:26Z-
dc.date.available2026-09-21T13:12:26Z-
dc.date.issued2008-
dc.identifier.citationFormalized Mathematics, Volume 16, Issue 4, 2008, Pages 297-303pl
dc.identifier.issn1426-2630-
dc.identifier.urihttp://hdl.handle.net/11320/21073-
dc.description.abstractIn this paper I present the Jordan Matrix Decomposition Theorem which states that an arbitrary square matrix M over an algebraically closed field can be decomposed into the form M=SJS−1 where S is an invertible matrix and J is a matrix in a Jordan canonical form, i.e. a special type of block diagonal matrix in which each block consists of Jordan blocks (see [13]).pl
dc.language.isoenpl
dc.publisherUniversity of Białystokpl
dc.rightsAttribution-ShareAlike 4.0 Internationalpl
dc.rights.urihttps://creativecommons.org/licenses/by-sa/4.0/-
dc.titleJordan Matrix Decompositionpl
dc.typeArticlepl
dc.rights.holder© 2009 Karol Pąk, published by University of Białystokpl
dc.rights.holderThis work is licensed under the Creative Commons License.pl
dc.identifier.doi10.2478/v10037-008-0036-9-
dc.description.AffiliationInstitute of Computer Science, University of Białystok, Polandpl
dc.description.referencesJesse Alama. The rank+nullity theorem. Formalized Mathematics, 15(3):137–142, 2007.pl
dc.description.referencesGrzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377–382, 1990.pl
dc.description.referencesGrzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41–46, 1990.pl
dc.description.referencesGrzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finitesequences. Formalized Mathematics, 1(1):107–114, 1990.pl
dc.description.referencesCzesław Byliński. Binary operations applied to finite sequences. Formalized Mathematics, 1(4):643–649, 1990.pl
dc.description.referencesCzesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529–536, 1990.pl
dc.description.referencesCzesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.pl
dc.description.referencesCzesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153–164, 1990.pl
dc.description.referencesCzesław Byliński. The modification of a function by a function and the iteration of the composition of a function. Formalized Mathematics, 1(3):521–527, 1990.pl
dc.description.referencesCzesław Byliński. Partial functions. Formalized Mathematics, 1(2):357–367, 1990.pl
dc.description.referencesCzesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47–53, 1990.pl
dc.description.referencesAgata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165–167, 1990.pl
dc.description.referencesGene H. Golub and J. H. Wilkinson. Ill-conditioned eigensystems and the computation of the Jordan normal form. SIAM Review, vol. 18, nr. 4, pp. 5788211;619, 1976.pl
dc.description.referencesKatarzyna Jankowska. Matrices. Abelian group of matrices. Formalized Mathematics, 2(4):475–480, 1991.pl
dc.description.referencesKatarzyna Jankowska. Transpose matrices and groups of permutations. Formalized Mathematics, 2(5):711–717, 1991.pl
dc.description.referencesAndrzej Kondracki. The Chinese Remainder Theorem. Formalized Mathematics, 6(4):573–577, 1997.pl
dc.description.referencesJarosław Kotowicz. Functions and finite sequences of real numbers. Formalized Mathematics, 3(2):275–278, 1992.pl
dc.description.referencesEugeniusz Kusak, Wojciech Leończuk, and Michał Muzalewski. Abelian groups, fieldsand vector spaces. Formalized Mathematics, 1(2):335–342, 1990.pl
dc.description.referencesRobert Milewski. Associated matrix of linear map. Formalized Mathematics, 5(3):339-345, 1996.pl
dc.description.referencesRobert Milewski. Fundamental theorem of algebra. Formalized Mathematics, 9(3):461-470, 2001.pl
dc.description.referencesMichał Muzalewski. Categories of groups. Formalized Mathematics, 2(4):563–571, 1991.pl
dc.description.referencesMichał Muzalewski. Rings and modules– part II. Formalized Mathematics, 2(4):579–585, 1991.pl
dc.description.referencesTakaya Nishiyama and Yasuho Mizuhara. Binary arithmetics. Formalized Mathematics, 4(1):83–86, 1993.pl
dc.description.referencesKarol P¸ak and Andrzej Trybulec. Laplace expansion. Formalized Mathematics, 15(3):143-150, 2007.pl
dc.description.referencesKarol Pąk. Block diagonal matrices. Formalized Mathematics, 16(3):259–267, 2008.pl
dc.description.referencesKarol Pąk. Eigenvalues of a linear transformation. Formalized Mathematics, 16(4):289-295, 2008.pl
dc.description.referencesKarol Pąk. Linear map of matrices. Formalized Mathematics, 16(3):269–275, 2008.pl
dc.description.referencesAndrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329–334, 1990.pl
dc.description.referencesAndrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1):115–122, 1990.pl
dc.description.referencesWojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821–827, 1990.pl
dc.description.referencesWojciech A. Trybulec. Linear combinations in vector space. Formalized Mathematics, 1(5):877–882, 1990.pl
dc.description.referencesWojciech A. Trybulec. Subspaces and cosets of subspaces in vector space. Formalized Mathematics, 1(5):865–870, 1990.pl
dc.description.referencesWojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291–296, 1990.pl
dc.description.referencesEdmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73–83, 1990.pl
dc.description.referencesXiaopeng Yue, Xiquan Liang, and Zhongpin Sun. Some properties of some special matrices. Formalized Mathematics, 13(4):541–547, 2005.pl
dc.description.referencesKatarzyna Zawadzka. The sum and product of finite sequences of elements of a field. Formalized Mathematics, 3(2):205–211, 1992.pl
dc.description.referencesKatarzyna Zawadzka. The product and the determinant of matrices with entries in a field. Formalized Mathematics, 4(1):1–8, 1993.pl
dc.identifier.eissn1898-9934-
dc.description.volume16pl
dc.description.issue4pl
dc.description.firstpage297pl
dc.description.lastpage303pl
dc.identifier.citation2Formalized Mathematicspl
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