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Title: On systems of linear algebraic equations in the Colombeau algebra (English)
Author: Ligęza, J.
Author: Tvrdý, M.
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959
Volume: 124
Issue: 1
Year: 1999
Pages: 1-14
Summary lang: English
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Category: math
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Summary: From the fact that the unique solution of a homogeneous linear algebraic system is the trivial one we can obtain the existence of a solution of the nonhomogeneous system. Coefficients of the systems considered are elements of the Colombeau algebra $\overline{\Bbb R}$ of generalized real numbers. It is worth mentioning that the algebra $\overline{\Bbb R}$ is not a field. (English)
Keyword: Colombeau algebra
Keyword: system of linear equations
Keyword: generalized real numbers
MSC: 15A06
MSC: 46F30
MSC: 46F99
idZBL: Zbl 0940.46022
idMR: MR1687437
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Date available: 2009-09-24T21:34:24Z
Last updated: 2015-09-15
Stable URL: http://hdl.handle.net/10338.dmlcz/125977
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Reference: [1] Colombeau J. F.: Elementary Introduction to New Generalized Functions.North Holland, Amsterdam, New York, Oxford, 1985. Zbl 0584.46024, MR 0808961
Reference: [2] Ligęza J.: Generalized solutions of boundary value problems for ordinary linear differential equations of second order in the Colombeau algebra.Dissertationes Mathematicae (Different aspect of differentiability) 340 (1995), 183-194. Zbl 0837.34026, MR 1342577
Reference: [3] Mc Cay N.H.: Rings and Ideals.The Carus Mathematical Monographs (Nr. 8), Baltimore, 1948.
Reference: [4] Przeworska-Rolewicz D.: Algebraic Analysis.PWN-Polish Scientific Publishers & D. Reidel Publishing Company, Warszawa, 1988. Zbl 0696.47002, MR 0945395
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