In this paper, a new approach to the solution of the inverse eigenvalue problem for symmetric matrices is obtained by means of linearization of the Lie group SO(n). The method formulated is motivated by an earlier approach which used classical Newton’s method to solve inverse eigenvalue problem for symmetric matrices. In both the cases, initialization of the iteration is implemented utilizing a related singular symmetric matrix. Numerical illustration for the case of 2 × 2 symmetric matrices is presented. Comparing the results of the computation, it was found that the two methods were in agreement.

inverse eigenvalue problem, symmetric matrices, Lie group SO(n), linearization.

Received: December 10, 2023; Accepted: March 1, 2024; Published: April 10, 2024

How to cite this article: Emmanuel Akweittey, Kwasi B. Gyamfi, F. T. Oduro and Y. E. Ayekple, Inverse eigenvalue problem for symmetric matrices in the context of the Lie group SO(n), JP Journal of Algebra, Number Theory and Applications 63(3) (2024), 247-263. http://dx.doi.org/10.17654/0972555524015

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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