On the Theory of Infinite Systems of Linear Algebraic EquationsF.M. Fedorov (pp. 202-212)
Abstract.The work provides an overview of the authors papers, which formed the basis of the new theory of general infinite systems of linear algebraic equations. In these papers the author extended the Gaussian elimination and Cramers rule to infinite systems. The special particular solution, so-called strictly particular solution, of inhomogeneous infinite systems was received. This strictly particular solution is written as a series. The divergence of this series demonstrates incompatibility of the original system. The necessary and sufficient conditions for the existence of nontrivial solutions of the homogeneous infinite systems are considered.
Keywords:infinite systems, rank and decrement, infinite matrices and determinants, strictly particular solution.