Contents V.10, N.2, 2019

  • 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 fi nite 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 infi nite system of linear algebraic equations. We give a concept of a fundamental solution of a homogeneous infi nite 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

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

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