Geodesic
On systems of linear algebraic equations in the Colombeau algebra
Mathematica Bohemica, Tome 124 (1999) no. 1, pp. 1-14

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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.
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.
DOI : 10.21136/MB.1999.125977
Classification : 15A06, 46F30, 46F99
Keywords: Colombeau algebra; system of linear equations; generalized real numbers 
Ligęza, J.; Tvrdý, M. On systems of linear algebraic equations in the Colombeau algebra. Mathematica Bohemica, Tome 124 (1999) no. 1, pp. 1-14. doi: 10.21136/MB.1999.125977
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