# The Quaternion Numbers

Formalized Mathematics (2006)

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

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topXiquan 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 -

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