НЕКОТОРЫЕ СПОСОБЫ ОПРЕДЕЛЕНИЯ СОВМЕСТНОСТИ СИСТЕМЫ ЛИНЕЙНЫХ АЛГЕБРАИЧЕСКИХ УРАВНЕНИЙ - Таджиев, Т.М. (SCIENCE and SOCIETY, 2020)
The article describes the application of the singular decomposition of a real matrix for solving an arbitrary system of linear algebraic equations and the linear least-squares problem, calculating determinants and not finding degenerate matrices, calculating eigenvalues and matrix rank. It is also shown that the singular decomposition of the matrix makes it easy to solve these problems in comparison with other methods for solving.
Keywords: singular decomposition; normal pseudo-solution; pseudoinverse matrix; nonsingular matrix; singular numbers; orthogonal matrix; Euclidean norm; eigenvalues; extended matrix