scholarly journals On Fibonacci quaternion matrix

2021 ◽  
Vol 27 (4) ◽  
pp. 236-244
Author(s):  
Serpil Halici ◽  
◽  
Ömür Deveci ◽  
Keyword(s):  
Quaternion Matrix ◽  
Fibonacci Quaternion

In this study, we have defined Fibonacci quaternion matrix and investigated its powers. We have also derived some important and useful identities such as Cassini’s identity using this new matrix.

scholarly journals Fundamental properties of extended Horadam numbers

2021 ◽  
Vol 27 (4) ◽  
pp. 219-235
Author(s):  
Gülsüm Yeliz Şentürk ◽  
◽  
Nurten Gürses ◽  
Salim Yüce ◽  
◽  
...  
Keyword(s):  
Quaternion Matrix ◽  
Fundamental Properties ◽  
Fibonacci Quaternion

In this study, we have defined Fibonacci quaternion matrix and investigated its powers. We have also derived some important and useful identities such as Cassini’s identity using this new matrix.

scholarly journals Cauchy matrix and Liouville formula of quaternion impulsive dynamic equations on time scales

2020 ◽  
Vol 18 (1) ◽  
pp. 353-377 ◽  
Author(s):  
Zhien Li ◽  
Chao Wang
Keyword(s):  
Time Scales ◽  
Quaternion Algebra ◽  
Matrix Exponential ◽  
Dynamic Equations ◽  
Necessary Condition ◽  
Quaternion Matrix ◽  
Exponential Functions ◽  
Cauchy Matrix ◽  
Adjoint Matrix ◽  
Sufficient And Necessary Condition

Abstract In this study, we obtain the scalar and matrix exponential functions through a series of quaternion-valued functions on time scales. A sufficient and necessary condition is established to guarantee that the induced matrix is real-valued for the complex adjoint matrix of a quaternion matrix. Moreover, the Cauchy matrices and Liouville formulas for the quaternion homogeneous and nonhomogeneous impulsive dynamic equations are given and proved. Based on it, the existence, uniqueness, and expressions of their solutions are also obtained, including their scalar and matrix forms. Since the quaternion algebra is noncommutative, many concepts and properties of the non-quaternion impulsive dynamic equations are ineffective, we provide several examples and counterexamples on various time scales to illustrate the effectiveness of our results.

On Fibonacci spinors

2020 ◽  
Vol 17 (04) ◽  
pp. 2050065
Author(s):  
Tülay Eri̇şi̇r ◽  
Mehmet Ali̇ Güngör
Keyword(s):  
Quaternion Algebra ◽  
Quaternion Matrix ◽  
Spinor Structure

Spinors are used in physics quite extensively. Basically, the forms of use include Dirac four-spinors, Pauli three-spinors and quaternions. Quaternions in mathematics are essentially equivalent to Pauli spin matrices which can be generated by regarding a quaternion matrix as compound. The goal of this study is also the spinor structure lying in the basis of the quaternion algebra. In this paper, first, we have introduced spinors mathematically. Then, we have defined Fibonacci spinors using the Fibonacci quaternions. Later, we have established the structure of algebra for these spinors. Finally, we have proved some important formulas such as Binet and Cassini formulas which are given for some series of numbers in mathematics for Fibonacci spinors.

scholarly journals A Real Representation Method for Solving Yakubovich-j-Conjugate Quaternion Matrix Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Caiqin Song ◽  
Jun-e Feng ◽  
Xiaodong Wang ◽  
Jianli Zhao
Keyword(s):  
Matrix Equation ◽  
Equivalent Form ◽  
Closed Form Solution ◽  
Coefficient Matrix ◽  
Form Solution ◽  
Complex Conjugate ◽  
Quaternion Matrix ◽  
Real Representation ◽  
Quaternion Matrix Equation ◽  
Representation Method

A new approach is presented for obtaining the solutions to Yakubovich-j-conjugate quaternion matrix equationX−AX^B=CYbased on the real representation of a quaternion matrix. Compared to the existing results, there are no requirements on the coefficient matrixA. The closed form solution is established and the equivalent form of solution is given for this Yakubovich-j-conjugate quaternion matrix equation. Moreover, the existence of solution to complex conjugate matrix equationX−AX¯B=CYis also characterized and the solution is derived in an explicit form by means of real representation of a complex matrix. Actually, Yakubovich-conjugate matrix equation over complex field is a special case of Yakubovich-j-conjugate quaternion matrix equationX−AX^B=CY. Numerical example shows the effectiveness of the proposed results.

QUATERNION BASED COLOR IMAGE QUALITY ASSESSMENT INDEX

2011 ◽  
Vol 11 (02) ◽  
pp. 195-206 ◽  
Author(s):  
YUQING WANG ◽  
MING ZHU ◽  
HAOCHEN PANG ◽  
YONG WANG
Keyword(s):  
Image Quality Assessment ◽  
Color Image ◽  
Structural Similarity ◽  
Singular Value ◽  
Reference Image ◽  
Quaternion Matrix ◽  
Color Information ◽  
Assessment Index ◽  
Local Variance ◽  
Visual Characteristics

A quaternion model for describing color image is proposed in order to evaluate its quality. Local variance distribution of luminance layer is calculated. Color information is taken into account by using quaternion matrix. The description method is a combination of luminance layer and color information. The angle between the singular value feature vectors of the quaternion matrices corresponding to the reference image and the distorted image is used to measure the structural similarity of the two color images. When the reference image and distorted images are of unequal size it can also assess their quality. Results from experiments show that the proposed method is better consistent with the human visual characteristics than MSE, PSNR and MSSIM. The resized distorted images can also be assessed rationally by this method.

Full Quaternion Matrix and Random Projection for Bimodal Face Template Protection

2021 ◽  
pp. 374-383
Author(s):  
Zihan Xu ◽  
Zhuhong Shao ◽  
Yuanyuan Shang ◽  
Zhongshan Ren
Keyword(s):  
Random Projection ◽  
Quaternion Matrix ◽  
Template Protection
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