Page 301 - KUATERNİYONLAR VE GEOMETRİ

300 Kuaterniyonlar ve Geometri ­ Mustafa Özdemir

5. Kösal, H. H., Tosun M., Some equivalence relations and results over the commutative quaternions and their
matrices.Analele Universitatii" Ovidius" Constanta­Seria Matematica 25.3 (2017): 125­142.
6. Kösal, H. H., Akyigit M., Tosun M. Consimilarity of commutative quaternion matrices." Miskolc
Mathematical Notes 16.2 (2015): 965­977.
7. Catoni, Francesco. "Commutative (Segre’s) Quaternion Fields and Relation with Maxwell Equations."
Advances in Applied Clifford Algebras 18.1 (2008): 9­28.
8. Hidayet Hüda Kösal, Komütatif kuaterniyonların matrisleri üzerine, Doktora tezi, 2016.

Elipsoidal ve Hiperboloidal Kuaterniyonlar
1. Özdemir, Mustafa. "An alternative approach to elliptical motion." Advances in Applied Clifford Algebras
26.1 (2016): 279­304.
2. Özdemir, Mustafa. "Elliptic Quaternions and Generating Elliptical Rotation Matrices." (2016).
3. Simsek, Hakan, and Mustafa Özdemir. "Generating hyperbolical rotation matrix for a given hyperboloid."
Linear Algebra and Its Applications 496 (2016): 221­245.
4. Simsek, Hakan, and Mustafa Özdemir. "Rotations on a lightcone in minkowski 3­Space." Advances in
Applied Clifford Algebras 27.3 (2017): 2841­285
5. Erdo˘ gdu Melek, "Reflections with Respect to Line and Hyperplane from Quaternionic Point of View." I˘ gdır
Üniversitesi Fen Bilimleri Enstitüsü Dergisi 9.3: 1612­1621.

Split Bikuaterniyonlar (Perplex Kuaterniyonlar)
1. https://en.wikipedia.org/wiki/Split­biquaternion
2. Cockle, J.: On a new imaginary in algebra 34:37–47. Lond. Edinb. Dublin Philos. Mag. 3(33), 435–9 (1849)
3. G. Sobczyk, Hyperbolic number plane, The college Mathematical Journal 26 (4), (1995), 268.
4. P. Fjelstad, Extending relativity via the perplex numbers, Am. J. Phys. 54 (1986), 416.
5. Harkin, A.A., Harkin, J.B.: Geometry of generalized complex numbers. Math. Mag. 77(2), 118–29 (2004)
6. F. Catoni, R. Cannata, V. Catoni and P. Zampetti, Hyperbolic trigonometry in two dimensional space­time
geometry, N. Cim. B 118 (2003), 475.
7. Kisil, V.V.: Geometry of Mobius Transformations: Elliptic, Parabolic and Hyperbolic Actions of SL2(R).
Imperial College Press, London (2012)
8. I. M. Yaglom, A simple non­Euclidean geometry and its physical basis, SpringerVerlag, New York 1979.
9. Rooney, J, On the three types of complex number and planar transformations, Environ. Plan.B5, 89–99,1978.
10. Hasan Çakır, Hiperbolik sayılar ve hiperbolik sayı matrislerinin cebirsel ve geometrik uygulamaları, Y.Lisans
tezi, 2017.

Dejenere ­ Yarı Dejenere ­ Duble Dejenere Kuaterniyonlar
1. Yaglom, I.M.: Complex Numbers in Geometry. Academic, New York (1968)
2. Rosenfeld, B.: Geometry of Lie Groups. Kluwer Academic, Dordrect (1997)
3. Inalcık, A.: Similarity and semi­similarity relations on the degenerate quaternions, pseudodegenerate
quaternions and doubly degenerate quaternions. Adv. Appl. Cliff. Algebras 27(2), 1329–1341 (2017)
4. Mortezaasl H., Jafari M., A study on Semi­quaternions Algebra in Semi­Euclidean 4­space, Mathematical
Science and Applications E­Notes, Vol. 1/2,(2013) 20­27.
5. Jafari, M.: Split semi­quaternions algebra in semi­Euclidean 4­space. Cumhuriyet Sci. J. 36(1), 70–77 (2015)
6. Yasemin Alagöz and Gözde Özyurt, Real and Hyperbolic Matrices of Split Semi Quaternions, Adv. Appl.
Clifford Algebras (2019) 29:53.
7. Mortazaasl, Hamid. "A study on semi­quaternions algebra in semi­Euclidean 4­space." Mathematical
sciences and applications E­notes 1.2 (2013): 20­27.

Tam Dejenere Kuaterniyonlar (Dual veya Null Kuaterniyonlar)
1. Ercan, Zeynep, and Salim Yüce. "On properties of the dual quaternions." European Journal of Pure and
Applied Mathematics 4.2 (2011): 142­146.
2. Yaylı y., Tutuncu E.E., Generalized Galilean Transformations and Dual Quaternions, Scientia Magna, Vol.5,
no.1 (2009) 94­100