Author(s)

Albert Iskhakov¹, Sergey Skovpen²

¹Department of Innovation Development, Joint Company “Research and Production Corporation ‘Space Monitoring Systems, Information & Control and Electromechanical Complexes’ named after A.G. Iosifian”, Moscow, Russia.
²Department of Ship Electricity and Automatics, Northern (Arctic) Federal University, Severodvinsk, Russia.

Contrary to the opinion about approximation nature of a simple-iteration method, the exact solution of a system of linear algebraic equations (SLAE) in a finite number of iterations with a stationary matrix is demonstrated. We present a theorem and its proof that confirms the possibility to obtain the finite process and imposes the requirement for the matrix of SLAE. This matrix must be unipotent, i.e. all its eigenvalues to be equal to 1. An example of transformation of SLAE given analytically to the form with a unipotent matrix is presented. It is shown that splitting the unipotent matrix into identity and nilpotent ones results in Cramer’s analytical formulas in a finite number of iterations.

System of Linear Algebraic Equations (SLAE), Nilpotent Matrix, Unipotent Matrix, Eigenvalue Assignment, Finite Iterative Process, Cramer’s Formulas

Iskhakov, A. and Skovpen, S. (2019) On the Deepest Fallacy in the History of Mathematics: The Denial of the Postulate about the Approximation Nature of a Simple-Iteration Method and Iterative Derivation of Cramer’s Formulas. Applied Mathematics, 10, 371-382. doi: 10.4236/am.2019.106027.