Geodesic
A sufficient condition of solutions existence for infinite systems of algebraic equations
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 16 (2016) no. 3, pp. 85-97

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The sufficient condition for existence of strictly particular solution of infinite system of linear algebraic equations is obtained by the use of double series theory. We expanded the determinant of Gaussian infinite matrix along the row as the result we obtained the series of infinite determinant. We proved the convergence theorems for this series of infinite determinant. We gave some an examples of applying this sufficient condition.
Keywords: infinite system, Gaussian infinite determinant, strictly particular solution, infinite Cramer's determinant.
Mots-clés : Gaussian infinite matrix 
@article{VNGU_2016_16_3_a7,
     author = {F. M. Fedorov},
     title = {A sufficient condition of solutions existence for infinite systems of algebraic equations},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {85--97},
     publisher = {mathdoc},
     volume = {16},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2016_16_3_a7/}
}
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F. M. Fedorov. A sufficient condition of solutions existence for infinite systems of algebraic equations. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 16 (2016) no. 3, pp. 85-97. http://geodesic.mathdoc.fr/item/VNGU_2016_16_3_a7/