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DESIGNING AND DETAILING OF BUILDING SYSTEMS. MECHANICS IN CIVIL ENGINEERING

Polynomial matrix symbols

Vestnik MGSU 9/2012
  • Myasnikov Aleksey Georgievich - Moscow State University of Civil Engineering (MGSU) Candidate of Physical and Mathematical Sciences, Associate Professor, Department of Higher Mathematics, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoye shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Zavadskaya Elena Petrovna - Moscow State University of Civil Engineering (MGSU) student, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 124 - 128

The operator symbol is usually its image at homomorphy into some function algebra or even into other operator algebras. In this case it is usually supposed, that the kernel of homomorphism is an ideal of rather continuous operators. In this case for Fredholm property of an operator the inversibility of its symbol is needed and enough. The authors consider the algebra generated by a complex matrix. The authors proved the existence and uniqueness of random matrix representation in the form of the sum of nilpotent matrix and linear combination of minimal idempotent matrixes combination.
The obtained results allow generalization for infinite-dimensional operators and can be used in systems of linear differential equations and in mathematical statistics.

DOI: 10.22227/1997-0935.2012.9.124 - 128

References
  1. Gokhberg I.Ts., Krupnik N.Ya. Vvedenie v teoriyu odnomernykh singulyarnykh integral’nykh operatorov [Introduction into the Theory of One-dimentional Singular Integral Operators]. Kishinev, Shtiintsa Publ., 1973, 428 p.
  2. Myasnikov A.G., Sazonov L.I. Singulyarnye integral’nye operatory s nekarlemanovskim sdvigom [Singular Integral Operators with a non-Carleman shift]. Izvestiya Vuzov. Matematica. [Bulletins of Institutions of Higher Education. Mathematics]. 1980, no. 3, pp. 22—31.
  3. Khelemskiy A.Ya. Banakhovy i polinormirovannye algebry: obshchaya teoriya, predstavleniya, gomologii. [Banach and Polynormed Algebras: General Theory, Representations, Homologies]. Moscow, Nauka Publ., 1989, 464 p.
  4. Causa A. Some Remarks in Linear Spaces îf Nilpotent Matrices. Le Matematiche, 1998, vol. LIII, pp. 23—32.
  5. DeMarr R. Nonnegative Idempotent Matrices. Proc. Amer. Math. Soc. 1974, vol. 45, no. 2, pp. 185—188.
  6. Horn R.A., Johnson Ch.R. Matrichnyy analiz [Matrix Analysis]. Moscow, Mir Publ., 1989, 654 p.

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