MATRIX THEORY OVER DGC NUMBERS-Reference-Cited by-同舟云学术

MATRIX THEORY OVER DGC NUMBERS

Published:2023-03-30 Issue:1 Volume:23 Page:209-228
ISSN:2068-3049
Container-title:Journal of Science and Arts
language:en
Short-container-title:J. Sci. Arts

Author:

GÜRSES NURTEN¹,ŞENTÜRK GÜLSÜM YELİZ²

Affiliation:

1. Yildiz Technical University, Faculty of Arts and Sciences, Department of Mathematics, 34220 Istanbul, Türkiye.

2. Istanbul Gelişim University, Faculty of Engineering and Architecture, Department of Computer Engineering, 34310 Istanbul, Türkiye.

Abstract

Classical matrix theory for real, complex and hypercomplex numbers is a well-known concept. Is it possible to construct matrix theory over dual-generalized complex (DGC) matrices? The answer to this question is given in this paper. The paper is constructed as follows. Firstly, the fundamental concepts for DGC matrices are introduced and DGC special matrices are defined. Then, theoretical results related to eigenvalues/eigenvectors are obtained and universal similarity factorization equality (USFE) regarding to the dual fundamental matrix are presented. Also, spectral theorems for Hermitian and unitary matrices are introduced. Finally, due to the importance of unitary matrices, a method for finding a DGC unitary matrix is stated and examples for spectral theorem are given.

Publisher

Valahia University of Targoviste - Journal of Science and Arts

Subject

General Earth and Planetary Sciences,General Environmental Science

Reference36 articles.

1. Yaglom, I. M., Complex numbers in geometry, Academic Press, New York, 1968.

2. Fjelstad, P., American Journal of Physics, 54, 416, 1986.

3. Sobczyk, G., The College Mathematics Journal, 26, 268, 1995.

4. Yaglom, I. M., A simple non-Euclidean geometry and its physical basis, Springer-Verlag, New York, 1979.

5. Pennestrì, E., Stefanelli, R., Multibody System Dynamics, 18, 323, 2007.

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