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A sufficient condition of solutions existence for infinite systems of algebraic equations
F. M. Fedorovab a Research Institute of Mathematics of North-Eastern Federal University named after M. K. Amosov
b Novosibirsk State University
Abstract:
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 matrix, Gaussian infinite determinant, strictly particular solution, infinite Cramer's determinant.
Received: 25.10.2015
Citation:
F. M. Fedorov, “A sufficient condition of solutions existence for infinite systems of algebraic equations”, Sib. J. Pure and Appl. Math., 16:3 (2016), 85–97; J. Math. Sci., 230:1 (2018), 36–45
Linking options:
https://www.mathnet.ru/eng/vngu413 https://www.mathnet.ru/eng/vngu/v16/i3/p85
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Abstract page: | 185 | Full-text PDF : | 112 | References: | 29 |
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