ON THE WHOLE POSITIVE SOLUTION OF MATRIX EQUATION X n = A FOR MATRICES OF THE SECOND ORDER IN THE CASE OF NATURAL n

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Published: Sep 29, 2017
Keywords:
нелинейное матричное уравнение, аналитические методы, система нелинейных алгебраических уравнений, метод математической индукции, натуральные корни уравнения nonlinear matrix equation, analytical methods, the system of nonlinear algebraic equations, the method of mathematical induction, the natural roots of the equation

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K. YAKUTO
Vitebsk State University named after P.M. Masherov

Abstract

Possibilities of using analytical methods for finding positive integer solutions of nonlinear matrix equations are studied. Lemmas contain the conditions on the coefficients of the X matrix, expressed through the coefficients of the matrix A. These conditions are given in the form of a system of nonlinear equations of several unknowns. The simplest method of the solution of the matrix equation form n X = A for matrices of different orders in the case of positive integer n is proposed. Presented results are possible to use to find positive integer roots of second-order matrices for any n.

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How to Cite
YAKUTO, K. (2017). ON THE WHOLE POSITIVE SOLUTION OF MATRIX EQUATION X n = A FOR MATRICES OF THE SECOND ORDER IN THE CASE OF NATURAL n. Vestnik of Polotsk State University. Part C. Fundamental Sciences, (12), 109-119. Retrieved from https://journals.psu.by/fundamental/article/view/3475
Issue
No. 12 (2017)
Section
mathematics
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This work is licensed under a Creative Commons Attribution 4.0 International License.

References

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