Computation of canonical matrices for chains and cycles of linear mappings
DOI: 10.1016/J.LAA.2003.07.001
关键词: Linear algebra 、 Vector space 、 Computation 、 Complex space 、 Matrix pencil 、 Pure mathematics 、 Canonical form 、 Kronecker delta 、 Algebra 、 Unitary state 、 Mathematics 、 Geometry and topology 、 Algebra and Number Theory 、 Numerical analysis 、 Discrete Mathematics and Combinatorics
摘要: Van Dooren [Linear Algebra Appl. 27 (1979) 103] constructed an algorithm for the computation of all irregular summands in Kronecker’s canonical form a matrix pencil. The is numerically stable since it uses only unitary transformations. We construct matrices chain linear mappings V1—V2—⋯—Vt andextend Dooren’s to cycle mappings whereall Vi are complex vector spaces and each line denotes → or ←.
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sci-hub.se 参考文章(13)
Hyman Bass, Algebraic K-theory ,(1968)
Peter Gabriel, Andrei V. Roiter, Representations of Finite-Dimensional Algebras ,(1992)
Peter Donovan, Mary Ruth Freislich, The representation theory of finite graphs and associated algebras Carleton University. ,(1973)
Peter Gabriel, Unzerlegbare Darstellungen I Manuscripta Mathematica. ,vol. 6, pp. 71- 103 ,(1972) , 10.1007/BF01298413
G. Belitskii, Normal forms in matrix spaces Integral Equations and Operator Theory. ,vol. 38, pp. 251- 283 ,(2000) , 10.1007/BF01291714
J. Gelonch, The contragredient equivalence for several matrices: a set of invariants Linear Algebra and its Applications. ,vol. 291, pp. 37- 49 ,(1999) , 10.1016/S0024-3795(98)10212-4
L A Nazarova, REPRESENTATIONS OF QUIVERS OF INFINITE TYPE Mathematics of The Ussr-izvestiya. ,vol. 7, pp. 749- 792 ,(1973) , 10.1070/IM1973V007N04ABEH001975
Roger A. Horn, Dennis I. Merino, Contragredient equivalence: A canonical form and some applications Linear Algebra and its Applications. ,vol. 214, pp. 43- 92 ,(1995) , 10.1016/0024-3795(93)00056-6
P. Van Dooren, The computation of Kronecker's canonical form of a singular pencil Linear Algebra and its Applications. ,vol. 27, pp. 103- 140 ,(1979) , 10.1016/0024-3795(79)90035-1
Feliks Ruvimovich Gantmakher, None, The Theory of Matrices ,(1984)