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# Formalized Mathematics

### (a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

4 Issues per year

SCImago Journal Rank (SJR) 2016: 0.207
Source Normalized Impact per Paper (SNIP) 2016: 0.315

Open Access
Online
ISSN
1898-9934
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Volume 14, Issue 4

# The Quaternion Numbers

Xiquan Liang
/ Fuguo Ge
Published Online: 2008-06-13 | DOI: https://doi.org/10.2478/v10037-006-0020-1

## The Quaternion Numbers

In this article, we define the set H of quaternion numbers as the set of all ordered sequences q = <x,y,w,z> 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.

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Published Online: 2008-06-13

Published in Print: 2006-01-01

Citation Information: Formalized Mathematics, Volume 14, Issue 4, Pages 161–169, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630,

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