Jordan Matrix Decomposition

• Autorzy: Karol Pąk
• Języki publikacji: EN

Abstrakty

EN

In 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 [...] 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]).MML identifier: MATRIXJ2, version: 7.9.01 4.101.1015

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2008
• Tom: 16
• Numer: 4
• Strony: 297-303

Daty

wydano

2008-01-01

online

2009-03-20

Twórcy

autor

Karol Pąk

• Institute of Computer Science, University of Białystok, Poland

Bibliografia

• [1] Jesse Alama. The rank+nullity theorem. Formalized Mathematics, 15(3):137-142, 2007.
• [2] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.
• [3] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.
• [4] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
• [5] Czesław Byliński. Binary operations applied to finite sequences. Formalized Mathematics, 1(4):643-649, 1990.
• [6] Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.
• [7] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
• [8] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
• [9] Czesław 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.
• [10] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
• [11] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
• [12] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.
• [13] Gene 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.
• [14] Katarzyna Jankowska. Matrices. Abelian group of matrices. Formalized Mathematics, 2(4):475-480, 1991.
• [15] Katarzyna Jankowska. Transpose matrices and groups of permutations. Formalized Mathematics, 2(5):711-717, 1991.
• [16] Andrzej Kondracki. The Chinese Remainder Theorem. Formalized Mathematics, 6(4):573-577, 1997.
• [17] Jarosław Kotowicz. Functions and finite sequences of real numbers. Formalized Mathematics, 3(2):275-278, 1992.
• [18] Eugeniusz Kusak, Wojciech Leończuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990.
• [19] Robert Milewski. Associated matrix of linear map. Formalized Mathematics, 5(3):339-345, 1996.
• [20] Robert Milewski. Fundamental theorem of algebra. Formalized Mathematics, 9(3):461-470, 2001.
• [21] Michał Muzalewski. Categories of groups. Formalized Mathematics, 2(4):563-571, 1991.
• [22] Michał Muzalewski. Rings and modules - part II. Formalized Mathematics, 2(4):579-585, 1991.
• [23] Takaya Nishiyama and Yasuho Mizuhara. Binary arithmetics. Formalized Mathematics, 4(1):83-86, 1993.
• [24] Karol Pαk and Andrzej Trybulec. Laplace expansion. Formalized Mathematics, 15(3):143-150, 2007.
• [25] Karol Pąk. Block diagonal matrices. Formalized Mathematics, 16(3):259-267, 2008.
• [26] Karol Pąk. Eigenvalues of a linear transformation. Formalized Mathematics, 16(4):289-295, 2008.
• [27] Karol Pąk. Linear map of matrices. Formalized Mathematics, 16(3):269-275, 2008.
• [28] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990.
• [29] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1):115-122, 1990.
• [30] Wojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821-827, 1990.
• [31] Wojciech A. Trybulec. Linear combinations in vector space. Formalized Mathematics, 1(5):877-882, 1990.
• [32] Wojciech A. Trybulec. Subspaces and cosets of subspaces in vector space. Formalized Mathematics, 1(5):865-870, 1990.
• [33] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.
• [34] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.
• [35] Xiaopeng Yue, Xiquan Liang, and Zhongpin Sun. Some properties of some special matrices. Formalized Mathematics, 13(4):541-547, 2005.
• [36] Katarzyna Zawadzka. The sum and product of finite sequences of elements of a field. Formalized Mathematics, 3(2):205-211, 1992.
• [37] Katarzyna Zawadzka. The product and the determinant of matrices with entries in a field. Formalized Mathematics, 4(1):1-8, 1993.

Identyfikatory

DOI

10.2478/v10037-008-0036-9