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On systems of linear algebraic equations in the Colombeau algebra. (English) Zbl 0940.46022

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 \(\overline {\mathbb R}\) of generalized real numbers. It is worth mentioning that the algebra \(\overline {\mathbb R}\) is not a field.

MSC:

46F30 Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.)
15A06 Linear equations (linear algebraic aspects)
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