A note on elliptic biquaternions

Özen, Kahraman Esen; Tosun, Murat

doi:10.1063/1.5020482

Cited by 8 publications

(10 citation statements)

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“…Theorem (Özen and Tosun) Let

Q = A_{0} + A_{1} boldi + A_{2} boldj + A_{3} boldk \in H C_{p}

be given where

Q \notin C_{p}

. If

{A_{1}}^{2} + {A_{2}}^{2} + {A_{3}}^{2} \neq 0

, in this case,

Q \sim A_{0} + γ ((), Q) boldi

where the number

γ ((), Q)

is an elliptic number that satisfies the equality

γ^{2} ((), Q) = {A_{1}}^{2} + {A_{2}}^{2} + {A_{3}}^{2}

. If

{A_{1}}^{2} + {A_{2}}^{2} + {A_{3}}^{2} = 0

, in this case,

Q \sim A_{0} - \frac{1}{2} boldj + \frac{1}{2 \sqrt{(||, p)}} I boldk

. …”

Section: Preliminariesmentioning

confidence: 99%

“…Lastly, we recall some necessary properties of elliptic matrices. For more details, see Özen and Tosun and Kösal …”

Section: Preliminariesmentioning

confidence: 99%

“…For more details, see other works. 16,[20][21][22] Binary numbers or generalized complex numbers are introduced 21 as z = x + I (x, ∈ R), I 2 = p + Iq (p, q ∈ R),…”

Section: Preliminariesmentioning

confidence: 99%

“…22 There are some of studies on elliptic numbers in literature. [16][17][18][19][20][21][22][23][24][25] The elliptic biquaternion algebra is a four-dimensional vector space over C p . It is represented as…”

Section: Preliminariesmentioning

confidence: 99%

“…The readers are referred to previous studies. [16][17][18][19][20] This article is organized as follows. In Section 2, we review elliptic numbers and elliptic biquaternions and recall the fundamental concepts of elliptic matrices.…”

mentioning

confidence: 99%

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On the matrix algebra of elliptic biquaternions

Özen

Tosun

2019

Math Methods in App Sciences

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In this study, we introduce the concept of elliptic biquaternion matrices. Firstly, we obtain elliptic matrix representations of elliptic biquaternion matrices and establish a universal similarity factorization equality for elliptic biquaternion matrices. Afterwards, with the aid of these representations and this equality, we obtain various results on some basic topics such as generalized inverses, eigenvalues and eigenvectors, determinants, and similarity of elliptic biquaternion matrices. These valuable results may be useful for developing a perfect theory on matrix analysis over elliptic biquaternion algebra in the future.

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“…Theorem (Özen and Tosun) Let

Q = A_{0} + A_{1} boldi + A_{2} boldj + A_{3} boldk \in H C_{p}

be given where

Q \notin C_{p}

. If

{A_{1}}^{2} + {A_{2}}^{2} + {A_{3}}^{2} \neq 0

, in this case,

Q \sim A_{0} + γ ((), Q) boldi

where the number

γ ((), Q)

is an elliptic number that satisfies the equality

γ^{2} ((), Q) = {A_{1}}^{2} + {A_{2}}^{2} + {A_{3}}^{2}

. If

{A_{1}}^{2} + {A_{2}}^{2} + {A_{3}}^{2} = 0

, in this case,

Q \sim A_{0} - \frac{1}{2} boldj + \frac{1}{2 \sqrt{(||, p)}} I boldk

. …”

Section: Preliminariesmentioning

confidence: 99%

“…Lastly, we recall some necessary properties of elliptic matrices. For more details, see Özen and Tosun and Kösal …”

Section: Preliminariesmentioning

confidence: 99%

“…For more details, see other works. 16,[20][21][22] Binary numbers or generalized complex numbers are introduced 21 as z = x + I (x, ∈ R), I 2 = p + Iq (p, q ∈ R),…”

Section: Preliminariesmentioning

confidence: 99%