Fibonacci Generalized Quaternions

Akyiğit, Mahmut; Kösal, Hidayet Hüda; Tosun, Murat

doi:10.1007/s00006-014-0458-0

Cited by 55 publications

(23 citation statements)

References 10 publications

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“…In this section, we derive necessary and sufficient conditions for the existence of the X = ±X * , X = ±X , and X = ±X * solutions with ∈ {i, j, k} to the generalized quaternion matrix equation (2). We first give two lemmas that follow immediately from theorem 1.1 of Dmytryshyn and Kägström.…”

Section: The X = ±X ⋆ Solutions To Axb + Cxd = Ementioning

confidence: 99%

The generalized quaternion matrix equation AXB+CX^⋆D=E

Liu

Zhang

2020

Math Methods in App Sciences

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In this paper, we discuss the generalized quaternion matrix equation AXB+CX⋆D=E, where X⋆ is one of X, X*, the η‐conjugate or the η‐conjugate transpose of X with η∈{i,j,k}. Two new real representations of a generalized quaternion matrix are proposed. By using this method, the criteria for the existence and uniqueness of solutions to the mentioned matrix equation as well as the existence of X=± X⋆ solutions to the generalized quaternion matrix equation AXB+CXD=E are derived in a unified way.

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Section: The X = ±X ⋆ Solutions To Axb + Cxd = Ementioning

confidence: 99%

The generalized quaternion matrix equation AXB+CX^⋆D=E

Liu

Zhang

2020

Math Methods in App Sciences

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“…Theorem 3.3. Let f n1 and l n2 be a Fibonacci and a Lucas vector as defined in (1) and (2). Then, their vector product is given by…”

Section: Fibonacci and Lucas Vectorsmentioning

confidence: 99%

“…On the other hand, Horadam introduced and generalized Fibonacci quaternions [7]. Akyigit, Kösal and Tosun studied Fibonacci generalized quaternions and gave some properties [1]. Later, Flaut and Savin studied Fibonacci and Lucas quaternions [3].…”

Section: Introductionmentioning

confidence: 99%

On Fibonacci and Lucas Vectors and Quaternions

Kaya¹,

Önder²

2018

ujam

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In this study, first we investigate the Fibonacci vectors, Lucas vectors and their vector products considering two Fibonacci vectors, two Lucas vectors and one of each vector. We give some theorems for the mentioned vector products and then we give the conditions for such vectors to be perpendicular or parallel. We also introduce the area formulas for the parallelograms constructed by Fibonacci and Lucas vectors with respect to Fibonacci and Lucas numbers. Moreover, we determine some formulas for the cosine and sine functions of the angles between two Fibonacci vectors, two Lucas vectors and lastly a Fibonacci vector and a Lucas vector. Finally, we investigate the Fibonacci quaternions and Lucas quaternions. We give some corollaries regarding the quaternion products of two Fibonacci quaternions, two Lucas quaternions and one of each quaternion. We conclude with the result that the quaternion product of such quaternions is neither a Fibonacci quaternion nor a Lucas quaternion.

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“…In [12], Horadam introduced the Fibonacci quaternion sequence and such sequences have been studied in several papers (see, for example, [11,[13][14][15]). Also generalizations of the Fibonacci quaternions have been presented in the literature (see, for example, [1,9,19,22]).…”

Section: Introductionmentioning

confidence: 99%

Bicomplex k-Pell Quaternions

Catarino

2018

Comput. Methods Funct. Theory

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Fibonacci Generalized Quaternions

Cited by 55 publications

References 10 publications

The generalized quaternion matrix equation AXB+CX^⋆D=E

The generalized quaternion matrix equation AXB+CX^⋆D=E

On Fibonacci and Lucas Vectors and Quaternions

Bicomplex k-Pell Quaternions

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About

Fibonacci Generalized Quaternions

Cited by 55 publications

References 10 publications

The generalized quaternion matrix equation AXB+CX⋆D=E

The generalized quaternion matrix equation AXB+CX⋆D=E

On Fibonacci and Lucas Vectors and Quaternions

Bicomplex k-Pell Quaternions

Contact Info

Product

Resources

About

The generalized quaternion matrix equation AXB+CX^⋆D=E

The generalized quaternion matrix equation AXB+CX^⋆D=E