Preview

Informatics

Advanced search

ORTHOGONAL REPRESENTATION OF THE PROPER TRANSFORMATION OF A PERSYMMETRIC MATRIX BASED ON ROTATION OPERATORS

Abstract

The mathematical substantiation of the algorithm for synthesis of the proper transformation and finding the eigenvalue formulae of a persymmetric matrix of dimension N = 2 k ( k =1, 4 ) based on orthogonal rotation operators is given. The proposed algorithm made it possible to improve the author's approach to calculating eigenvalues based on numerical examples for the maximal dimension of matrices 64×64, resulting the possibility to obtain analytical relations for calculating the eigenvalues of the persymmetric matrix. It is shown that the proper transformation has a factorized structure in the form of a product of rotation operators, each of which is a direct sum of elementary Givens and Jacobian rotation matrices.

 

For citations:


Demko V.M. ORTHOGONAL REPRESENTATION OF THE PROPER TRANSFORMATION OF A PERSYMMETRIC MATRIX BASED ON ROTATION OPERATORS. Informatics. 2018;15(1):34-50. (In Russ.)

Views: 845


Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.


ISSN 1816-0301 (Print)
ISSN 2617-6963 (Online)