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Your search keyword '"KÖSAL, HIDAYET HÜDA"' showing total 3 results
Start Over Author "KÖSAL, HIDAYET HÜDA" Topic algebra
3 results on '"KÖSAL, HIDAYET HÜDA"'

1. Least-squares solutions of the reduced biquaternion matrix equation AX=B and their applications in colour image restoration.

Author

Kösal, Hidayet Hüda

Subjects
*IMAGE reconstruction, *COLOR, *EQUATIONS, *MATRICES (Mathematics), *ALGEBRA
Abstract

In this study, we derive the expressions of the minimal norm least-squares solution for the reduced biquaternion (RB) matrix equation AX=B by using the e 1 − e 2 form of RB matrices, and the Moore–Penrose generalized inverse. Moreover, we investigate their applications in colour image restoration. Therefore, many useful image restoration methods can be extended to reduced biquaternion algebra without separating the colour image into three channels. To prove the authenticity of our results and to distinguish them from existing ones, some illustrative examples are also given. [ABSTRACT FROM AUTHOR]

Published
2019
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2. On the Consimilarity of Split Quaternions and Split Quaternion Matrices

Author

Mahmut Akyiğit, Hidayet Hüda Kösal, Murat Tosun, Kosal, HH, Akyigit, M, Tosun, M, Sakarya Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü, Kösal, Hidayet Hüda, Akyiğit, Mahmut, and Tosun, Murat

Subjects
Algebra, 010102 general mathematics, 0103 physical sciences, General Materials Science, 010307 mathematical physics, 0101 mathematics, Quaternion, 01 natural sciences, Mathematics, Split-quaternion
Abstract

In this paper, we introduce the concept of consimilarity of split quaternions and split quaternion matrices. In his regard, we examine the solvability conditions and general solutions of the equations and in split quaternions and split quaternion matrices, respectively. Moreover, coneigenvalue and coneigenvector are defined for split quaternion matrices. Some consequences are also presented.

Published
2016

3. Fibonacci Generalized Quaternions

Author

Hidayet Hüda Kösal, Murat Tosun, Mahmut Akyiğit, Akyigit, M, Kosal, HH, Tosun, M, Sakarya Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü, Akyiğit, Mahmut, Kösal, Hidayet Hüda, and Tosun, Murat

Subjects
Combinatorics, Algebra, Fibonacci number, Lucas number, Lucas sequence, Applied Mathematics, Fibonacci polynomials, Fibonacci and Lucas numbers, Generalized quaternions, Fibonacci and Lucas Generalized quaternions, Pisano period, Quaternion, Classical Hamiltonian quaternions, Mathematics
Abstract

In this paper, the Fibonacci generalized quaternions are introduced. We use the well-known identities related to the Fibonacci and Lucas numbers to obtain the relations regarding these quaternions. Furthermore, the Fibonacci generalized quaternions are classified by considering the special cases of quaternionic units.

Published
2014

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