The Quaternion Numbers

Xiquan Liang; Fuguo Ge

Formalized Mathematics (2006)

  • Volume: 14, Issue: 4, page 161-169
  • ISSN: 1426-2630

Abstract

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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.

How to cite

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Xiquan Liang, and Fuguo Ge. "The Quaternion Numbers." Formalized Mathematics 14.4 (2006): 161-169. <http://eudml.org/doc/267069>.

@article{XiquanLiang2006,
abstract = {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.},
author = {Xiquan Liang, Fuguo Ge},
journal = {Formalized Mathematics},
language = {eng},
number = {4},
pages = {161-169},
title = {The Quaternion Numbers},
url = {http://eudml.org/doc/267069},
volume = {14},
year = {2006},
}

TY - JOUR
AU - Xiquan Liang
AU - Fuguo Ge
TI - The Quaternion Numbers
JO - Formalized Mathematics
PY - 2006
VL - 14
IS - 4
SP - 161
EP - 169
AB - 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.
LA - eng
UR - http://eudml.org/doc/267069
ER -

References

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