Rotations with unit timelike quaternions in Minkowski 3-space

Özdemir, Mustafa; Ergin, Abdullah Aziz

doi:10.1016/j.geomphys.2005.02.004

Cited by 103 publications

(75 citation statements)

References 4 publications

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“…It is nearby to identify a split quaternion a ∈ H S with a vector − → a ∈ R 4 2 (where R 4 2 is semi-Euclidean space [17]). We will denote such identification by the symbol i.e.…”

Section: Consimilarity Of Split Quaternionsmentioning

confidence: 99%

“…Complex consimilarity is an equivalence relation on C n×n and has been extensively studied [12]. The split quaternion holds an important place in differential geometry and structure theory of Lorentz Space [16], [17], and for this reason consimilarity relation will be defined for split quaternions. If a, b ∈ H S , generally ab = a b.…”

Section: Theoremmentioning

confidence: 99%

“…The split quaternions are a recently developing topic, since the split quaternions are used to express Lorentzian relations. Also, there are many studies on geometric and physical meaning of the split quaternions [16]- [17]. In [8], author studied equations ax = xb, ax = xb and x 2 = a, in algebras obtained by the Cayley-Dickson process.…”

Section: Introductionmentioning

confidence: 99%

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On the Consimilarity of Split Quaternions and Split Quaternion Matrices

Kösal

Akyiğit

Tosun

2016

Analele Universitatii "Ovidius" Constanta - Seria Matematica

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

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“…It is nearby to identify a split quaternion a ∈ H S with a vector − → a ∈ R 4 2 (where R 4 2 is semi-Euclidean space [17]). We will denote such identification by the symbol i.e.…”

Section: Consimilarity Of Split Quaternionsmentioning

confidence: 99%

Section: Theoremmentioning

confidence: 99%

See 1 more Smart Citation

On the Consimilarity of Split Quaternions and Split Quaternion Matrices

Kösal

Akyiğit

Tosun

2016

Analele Universitatii "Ovidius" Constanta - Seria Matematica

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“…The vector part of any space-like quaternions is space-like but the vector part of any time-like quaternion can be space-like or time-like. One can construct also polar forms of split quaternions [20]:…”

Section: Classification Of Split Quaternionsmentioning

confidence: 99%

“…The vector part of split quaternions, instead of the Euclidean 3-space, represents the (2+1)-Minkowski space-time [20]. Now we want to consider rotations performed by the unit split quaternions in a similar manner as Hamilton's unit quaternions do.…”

Section: Boostsmentioning

confidence: 99%

Split quaternions and particles in (2+1)-space

Gogberashvili

2014

Eur. Phys. J. C

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It is well known that quaternions represent rotations in 3D Euclidean and Minkowski spaces. However, the product by a quaternion gives rotation in two independent planes at once and to obtain single-plane rotations one has to apply half-angle quaternions twice from the left and on the right (with inverse). This 'double-cover' property is a potential problem in the geometrical application of split quaternions, since the (2+2)-signature of their norms should not be changed for each product. If split quaternions form a proper algebraic structure for microphysics, the representation of boosts in (2+1)-space leads to the interpretation of the scalar part of quaternions as the wavelengths of particles. The invariance of space-time intervals and some quantum behaviors, like noncommutativity and the fundamental spinor representation, probably also are algebraic properties. In our approach the Dirac equation represents the CauchyRiemann analyticity condition and two fundamental physical parameters (the speed of light and Planck's constant) emerge from the requirement of positive definiteness of the quaternionic norms.

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Real matrix representations of complex split quaternions with applications

Erdoğdu

Özdemir

2020

Math Methods in App Sciences

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In this paper, we introduce 8×8 real matrix representations of complex split quaternions. Then, the relations between real matrix representations of split and complex split quaternions are stated. Moreover, we investigate some linear split and complex split quaternionic equations with split Fibonacci and complex split Fibonacci quaternion coefficients. Finally, we also give some numerical examples as applications of real matrix representation of complex split quaternions.

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Rotations with unit timelike quaternions in Minkowski 3-space

Cited by 103 publications

References 4 publications

On the Consimilarity of Split Quaternions and Split Quaternion Matrices

On the Consimilarity of Split Quaternions and Split Quaternion Matrices

Split quaternions and particles in (2+1)-space

Real matrix representations of complex split quaternions with applications

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