In this article, we define the set H of quaternion numbers as the set of all ordered sequences q = where x,y,w and z are real numbers. The addition, difference and multiplication of the quaternion numbers are also defined. We define the real and imaginary parts of q and denote this by x = ℜ(q), y = ℑ1(q), w = ℑ2(q), z = ℑ3(q). We define the addition, difference, multiplication again and denote this operation by real and three imaginary parts. We define the conjugate of q denoted by q*' and the absolute value of q denoted by |q|. We also give some properties of quaternion numbers.
@article{bwmeta1.element.doi-10_2478_v10037-006-0020-1,
author = {Xiquan Liang and Fuguo Ge},
title = {The Quaternion Numbers},
journal = {Formalized Mathematics},
volume = {14},
year = {2006},
pages = {161-169},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10037-006-0020-1}
}
Xiquan Liang; Fuguo Ge. The Quaternion Numbers. Formalized Mathematics, Tome 14 (2006) pp. 161-169. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10037-006-0020-1/
[1] Grzegorz Bancerek. Arithmetic of non-negative rational numbers. To appear in Formalized Mathematics. | Zbl 06213832
[2] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
[3] Czesław Byliński. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.
[4] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
[5] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
[6] Czesław Byliński. The modification of a function by a function and the iteration of the composition of a function. Formalized Mathematics, 1(3):521-527, 1990.
[7] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
[8] Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.
[9] Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.
[10] Wojciech Leończuk and Krzysztof Prażmowski. Incidence projective spaces. Formalized Mathematics, 2(2):225-232, 1991. | Zbl 0741.51010
[11] Andrzej Trybulec. Introduction to arithmetics. To appear in Formalized Mathematics.
[12] Andrzej Trybulec. Subsets of complex numbers. To appear in Formalized Mathematics.
[13] Andrzej Trybulec. Enumerated sets. Formalized Mathematics, 1(1):25-34, 1990.
[14] Andrzej Trybulec. Tarski Grothendieck set theory. Formalized Mathematics, 1(1):9-11, 1990.
[15] Andrzej Trybulec. and Czesław Byliński. Some properties of real numbers. Formalized Mathematics, 1(3):445-449, 1990.
[16] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
[17] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.
[18] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.