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In current paper we present comparative analysis of methodological and computational aspects of traditional methods for solving basic linear algebra problems. It is shown that the ``critical components'' method, also referred to as ``the uncertainty principle in linear algebra'', introduced in [4] and later developed in papers referenced in [1]-[3], has an advantage over fundamental concepts, lying beneath such well-known methods as regularization, singular decomposition and iterative QR-decomposition with deflation. Analogies are drawn between the uncertainty relations in linear algebra and in quantum mechanics. We discuss the role of the established uncertainty relations in generating new numerical methods for finding effective stable approximations to the solutions of ill-posed linear algebra problems. begin{thebibliography}{} bibitem{[1]}{G.A. Emel'yanenko, Doctor's Dissertation, CC SB AS USSR, Novosibirsk, 1992, JINR 11-92-4, Dubna 1992 /in Russian/} bibitem{[2]}{G.A. Emel'yanenko, M.G. Emelianenko, T.T.Rakhmonov et al ; JINR preprint, E11-98-302, Dubna, 1998.} bibitem{[3]}{E. B. Dushanov, Candidate's Dissertation, JINR 11-2001-114, Dubna, 2001 /in Russian/} bibitem{[4]}{G.A. Emel'yanenko, JINR preprints: P11-86-531, Dubna 1986, P11-85-34, Dubna 1985 /in Russian/} end{thebibliography}

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