| 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 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
124 |
| Issue:
|
1 |
| Year:
|
1999 |
| Pages:
|
1-14 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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 |
| DOI:
|
10.21136/MB.1999.125977 |
| . |
| Date available:
|
2009-09-24T21:34:24Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/125977 |
| . |
| 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 |
| . |
