ON REMARKABLE RELATIONS AND THE PASSAGE TO THE LIMIT IN THE THEORY OF INFINITE SYSTEMS II

*F.M. FEDOROV, S.V. POTAPOVA (pp. 154-174)*#### Abstract

We have found solutions of homogeneous finite Gaussian system of linear algebraic equations with a degenerate matrix. These solutions are given by functional relations that allow us to pass to the limit from finite truncated systems to an infinite system of linear algebraic equations. We give a concept of a fundamental solution of a homogeneous infinite system. This fundamental solution is given by Fedorovs formula. Fedorovs formula expresses the solution using Fedorovs determinant, which is similar to Cramers determinant for inhomogeneous systems.

#### Keywords

infinite system, homogeneous, inhomogeneous, method of reduction, strictly particular solution, Cramers rule, nontrivial solution, principal fundamental solution.