ON THE THEORY OF INFINITE SYSTEMS OF LINEAR ALGEBRAIC EQUATIONS

The work provides an overview of the author s 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 Cramer s 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.