On some applications of bilateral orthogonalization in computational algebra

In this article it is proved that the equations of sequential solution of a number of computational algebra problems are the consequences of equations of counter orthogonalization and biorthogonalization in Hilbert and Euclidean spaces. The basis of these equations is the known sequential method of direct Gram–Sonin–Schmidt orthogonalization. It is considered the problems related to matrix inversions, their triangular factorizations, and solving systems of linear algebraic equations.