On systems of linear algebraic equations in the Colombeau algebra

@article{Ligęza1999,
abstract = {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.},
author = {Ligęza, Jan, Tvrdý, Milan},
journal = {Mathematica Bohemica},
keywords = {Colombeau algebra; system of linear equations; generalized real numbers; Colombeau algebra; system of linear equations; generalized real numbers},
language = {eng},
number = {1},
pages = {1-14},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On systems of linear algebraic equations in the Colombeau algebra},
url = {http://eudml.org/doc/248461},
volume = {124},
year = {1999},
}

TY - JOUR
AU - Ligęza, Jan
AU - Tvrdý, Milan
TI - On systems of linear algebraic equations in the Colombeau algebra
JO - Mathematica Bohemica
PY - 1999
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 124
IS - 1
SP - 1
EP - 14
AB - 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.
LA - eng
KW - Colombeau algebra; system of linear equations; generalized real numbers; Colombeau algebra; system of linear equations; generalized real numbers
UR - http://eudml.org/doc/248461
ER -