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quaternion

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quaternion
quaternion (kwəˈtɜːnɪən) [ad. late L. quaternio, -iōn-em, f. quaternī four together: cf. obs. F. quaternion (Godef.).] 1. a. A group or set of four persons or things; spec. a set of four poems.1382 Wyclif Acts xii. 4 Bitakinge [him] to foure quaternyouns of Knyȝtis..for to kepe him. [Tindale and lat... Oxford English Dictionary
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Quaternion
A quaternion that equals its vector part is called a vector quaternion. Unit quaternion A unit quaternion is a quaternion of norm one. wikipedia.org
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Quaternion (poetry)
Quaternion is a poetry style in which the theme is divided into four parts. References External links Quaternion examples Poetic forms wikipedia.org
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quaternion product distributivity If you check the quaternion product derivation at wikipedia: < You can see that it is derived from a multiplication table between the quaternions 1,i,j,k. All books I have on the to...
The multiplication is defined, in fact, as the unique product which distributes along sums, behaves nicely with scalars and takes the correct values at the basic elements. That this _is_ actually such a multiplication is a simple result in linear algebra, similar to thaht which says that a linear ma...
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Quaternion (disambiguation)
Quaternion rotation Quaternion group, a non-abelian group of order 8 Symbols Imperial quaternions (heraldry of the Holy Roman Empire) Quaternion Quaternion (poetry), a style of poetry with four parts See also wikipedia.org
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The geometric interpretation of quaternion and Octanion Can anybody give me any useful link for the history of quaternion? The quaternion and Octanion are constructed but why other do not exist? What is the geometric ...
In the case of complex space we have two real perpendicular axex while in the case of Quaternion we have 2 complex axes and a quaternion is constructed
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Quaternion group - Wikipedia
In group theory, the quaternion group Q 8 (sometimes just denoted by Q) is a non-abelian group of order eight, isomorphic to the eight-element subset of the quaternions under multiplication. It is given by the group presentation. where e is the identity element and e commutes with the other elements of the group.
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Normalizing a quaternion How do I normalize a quaternion $$q=w + \mathbf ix + \mathbf jy + \mathbf kz = a + v$$ ? I already know: The normalized quaternion is called unit quaternion and can be calculated in this way:...
Yes, by its length or norm as it's also called. You get: $$U_q=\frac{w}{d} + \mathbf i \cdot \frac{x}{d} + \mathbf j \cdot \frac{y}{d} + \mathbf k \cdot \frac{z}{d}$$ where $d = ||q|| = \sqrt {w^2 + x^2 + y^2 + z^2} $ is the norm.
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Quaternion group
Generalized quaternion group A generalized quaternion group Q4n of order 4n is defined by the presentation for an integer , with the usual quaternion External links Quaternion groups on GroupNames Quaternion group on GroupProps Conrad, Keith. wikipedia.org
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Dual quaternion
The vector dot and cross operations can now be used to define the quaternion product of and as A dual quaternion is usually described as a quaternion Matrix form of dual quaternion multiplication The matrix representation of the quaternion product is convenient for programming quaternion computations wikipedia.org
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OpenCASCADE Quaternion - eryar - C++博客
There are several different ways we can express orientation and angular displacement in 3D. Here we discuss the three most important methods-matrices, Euler angles, and quaternions. ... 史银雪,陈洪,王荣静. 3D数学基础：图形与游戏开发. 清华大学出版社. 2005 . 8. 苏步青. 神奇的符号. 湖南少年儿童出版社. 2010 . www.cppblog.com
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Quaternion Eagle
The Quaternion Eagle (; ), also known as the Imperial Quaternion Eagle () or simply Imperial Eagle (), was an informal coat of arms of the Holy Roman Empire Introduced around 1510 by Hans Burgkmair, the Quaternion Eagle mixed two pre-existing concepts: the Imperial Quaternions and the Imperial Eagle (double-headed wikipedia.org
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A New Calculation Method of Quaternion Differential Equation for ...
Abstract: A new calculation method of quaternion differential equation, which is called three-subsample quaternion algorithm, is presented to solve the problem of low calculation accuracy of traditional quaternion algorithm by using the calculation process of three-subsample rotation vector algorithm for reference. In the calculation process, the higher derivative of rotation quaternion is ... www.co-journal.com
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Automorphisms of The Projective Quaternion Unimodular Group of Two ...
Let K be the skew field of rational quaternions. Let R={(a+bi+cj+dk)/2|a, b, c, d∈Z and have the same parity}, where Z denotes the ring of rational integers. R is a sabring of K and K is the quotient skew field of R. R is usually called the ring of quaternion integers.Let E denote the subgroup of GL_2(R) generated by all elements of the from (?) and(?)(s, t∈R). Denote the factor groups of ...
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CompilerDesign/quaternion.py at master · Aerotic/CompilerDesign
A compiler for self-defined program language. Contribute to Aerotic/CompilerDesign development by creating an account on GitHub.
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