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Meaning of "quaternion" in the English dictionary

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DICTIONARY
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ETYMOLOGY OF THE WORD QUATERNION

From Late Latin quaterniōn, from Latin quaternī four at a time.
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Etymology is the study of the origin of words and their changes in structure and significance.
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PRONUNCIATION OF QUATERNION

quaternion  [kwəˈtɜːnɪən] play
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GRAMMATICAL CATEGORY OF QUATERNION

noun
adjective
verb
adverb
pronoun
preposition
conjunction
determiner
exclamation
Quaternion is a noun.
A noun is a type of word the meaning of which determines reality. Nouns provide the names for all things: people, objects, sensations, feelings, etc.

WHAT DOES QUATERNION MEAN IN ENGLISH?

quaternion

Quaternion

In mathematics, the quaternions are a number system that extends the complex numbers. They were first described by Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. A feature of quaternions is that multiplication of two quaternions is noncommutative. Hamilton defined a quaternion as the quotient of two directed lines in a three-dimensional space or equivalently as the quotient of two vectors. Quaternions find uses in both theoretical and applied mathematics, in particular for calculations involving three-dimensional rotations such as in three-dimensional computer graphics and computer vision. In practical applications, they can be used alongside other methods, such as Euler angles and rotation matrices, or as an alternative to them depending on the application. In modern mathematical language, quaternions form a four-dimensional associative normed division algebra over the real numbers, and therefore also a domain. In fact, the quaternions were the first noncommutative division algebra to be discovered. The algebra of quaternions is often denoted by H, or in blackboard bold by .

Definition of quaternion in the English dictionary

The definition of quaternion in the dictionary is a generalized complex number consisting of four components, x = x0 + x1i + x2j + x3k, where x, x0… x3 are real numbers and i² = j² = k² = –1, ij = –ji = k, etc.

WORDS THAT RHYME WITH QUATERNION


Armenian
ɑːˈmiːnɪən
Athenian
əˈθiːnɪən
Bornean
ˈbɔːnɪən
Californian
ˌkælɪˈfɔːnɪən
Cameroonian
ˌkæməˈruːnɪən
eburnean
ɛˈbɜːnɪən
Fenian
ˈfiːnɪən
Ghanian
ˈɡɑːnɪən
Hibernian
haɪˈbɜːnɪən
Kiwanian
kɪˈwɑːnɪən
Magdalenian
ˌmæɡdəˈliːnɪən
Mancunian
mæŋˈkjuːnɪən
Melburnian
mɛlˈbɜːnɪən
Neptunian
nɛpˈtjuːnɪən
Oceanian
ˌəʊʃɪˈɑːnɪən
Ruthenian
ruːˈθiːnɪən
Saturnian
sæˈtɜːnɪən
Slovenian
sləʊˈviːnɪən
ternion
ˈtɜːnɪən
Tyrrhenian
tɪˈriːnɪən

WORDS THAT BEGIN LIKE QUATERNION

quat
quatch
quatercentenaries
quatercentenary
quatercentennial
quaternaries
quaternary
quaternary ammonium compound
quaternate
quaternionist
quaternities
quaternity
Quathlamba
quatorzain
quatorze
quatrain
quatre
Quatre Bras
quatrefeuille
quatrefoil

WORDS THAT END LIKE QUATERNION

a matter of opinion
communion
companion
credit union
customs union
dominion
European Union
Holy Communion
matter of opinion
minion
onion
opinion
pinion
public opinion
reunion
rugby union
second opinion
Soviet Union
the Union
union

Synonyms and antonyms of quaternion in the English dictionary of synonyms

SYNONYMS

Translation of «quaternion» into 25 languages

TRANSLATOR
online translator

TRANSLATION OF QUATERNION

Find out the translation of quaternion to 25 languages with our English multilingual translator.
The translations of quaternion from English to other languages presented in this section have been obtained through automatic statistical translation; where the essential translation unit is the word «quaternion» in English.

Translator English - Chinese

四元
1,325 millions of speakers

Translator English - Spanish

cuaternión
570 millions of speakers

English

quaternion
510 millions of speakers

Translator English - Hindi

चौका
380 millions of speakers
ar

Translator English - Arabic

المركب المتعدد
280 millions of speakers

Translator English - Russian

кватернионная
278 millions of speakers

Translator English - Portuguese

quatérnion
270 millions of speakers

Translator English - Bengali

চার বস্তুর সমষ্টি
260 millions of speakers

Translator English - French

quaternion
220 millions of speakers

Translator English - Malay

Quaternion
190 millions of speakers

Translator English - German

Quaternion
180 millions of speakers

Translator English - Japanese

クォータニオン
130 millions of speakers

Translator English - Korean

사원 수
85 millions of speakers

Translator English - Javanese

Quaternion
85 millions of speakers
vi

Translator English - Vietnamese

toán qua tec non
80 millions of speakers

Translator English - Tamil

quaternion
75 millions of speakers

Translator English - Marathi

चतुष्कोण
75 millions of speakers

Translator English - Turkish

kuaternion
70 millions of speakers

Translator English - Italian

quaternione
65 millions of speakers

Translator English - Polish

quaternion
50 millions of speakers

Translator English - Ukrainian

кватернионами
40 millions of speakers

Translator English - Romanian

cuaternion
30 millions of speakers
el

Translator English - Greek

quaternion
15 millions of speakers
af

Translator English - Afrikaans

viertal
14 millions of speakers
sv

Translator English - Swedish

kvaternionen
10 millions of speakers
no

Translator English - Norwegian

quaternion
5 millions of speakers

Trends of use of quaternion

TRENDS

TENDENCIES OF USE OF THE TERM «QUATERNION»

The term «quaternion» is quite widely used and occupies the 49.520 position in our list of most widely used terms in the English dictionary.
0
100%
FREQUENCY
Quite widely used
77
/100
The map shown above gives the frequency of use of the term «quaternion» in the different countries.
Principal search tendencies and common uses of quaternion
List of principal searches undertaken by users to access our English online dictionary and most widely used expressions with the word «quaternion».

FREQUENCY OF USE OF THE TERM «QUATERNION» OVER TIME

The graph expresses the annual evolution of the frequency of use of the word «quaternion» during the past 500 years. Its implementation is based on analysing how often the term «quaternion» appears in digitalised printed sources in English between the year 1500 and the present day.

Examples of use in the English literature, quotes and news about quaternion

EXAMPLES

10 ENGLISH BOOKS RELATING TO «QUATERNION»

Discover the use of quaternion in the following bibliographical selection. Books relating to quaternion and brief extracts from same to provide context of its use in English literature.
1
Visualizing Quaternions
The first part of the book focuses on visualizing quaternions to provide the intuition necessary to use them, and includes many illustrative examples to motivate why they are important—a beautiful introduction to those wanting to explore ...
Andrew J. Hanson, 2006
2
Quaternion Orders, Quadratic Forms, and Shimura Curves
Shimura curves are a far-reaching generalization of the classical modular curves.
Montserrat Alsina, Pilar Bayer i Isant, 2004
3
Generalized Quaternion Algebras and Cyclic Algebras
Finally, a cyclic algebra is a noncommutative algebra of dimension n2 over F, constructed from a Galois extension E/F.
Kresimir Lovric, 2006
4
Thetheory of Groups
The quaternion group has exactly 24 automorphism*. The generalized quaternion group of order 2» has exactly 2tn- ^automorphisms for n > 3. In the automorphism group A of the quaternion group, the inner automorphisms form an abelian ...
Hans Zassenhaus, 1958
5
Mechanics of Flight
Robinson (1958) described the advantages of the Euler-Rodrigues quaternion formulation over the Euler angle or the direction-cosine formulation almost 50 years ago. Most of his observations, obtained on analog computers, are still valid in ...
Warren F. Phillips, 2004
6
Springer Handbook of Robotics
Table 1.3 Conversions from angle-axis to unit quaternion representations of orientation and vice versa Angle-axis dw to unit quaternion (fa £\ £2 ^3)T: 6() = COS | 61 = wx sin | 62 = w ,, sin | 63 = to, sin Unit quaternion ( e =2cos-' € { £2 ^3) T to ...
Bruno Siciliano, Oussama Khatib, 2008
7
Quaternion and Clifford Fourier Transforms and Wavelets
Quaternion analysis, quaternion Fourier transform, quaternion FourierIStieltjes integral, Bochner theorem. 1. Introduction In a recent paper [5], we discussed special properties of the asymptotic behaviour of the quaternion Fourier transform  ...
Eckhard Hitzer, Stephen J. Sangwine, 2013
8
The Second Chinburg Conjecture for Quaternion Fields
Therefore the case of quaternion fields is a very interesting special case. In this case the Galois group, G(N/Q), is isomorphic to the quaternion group of order eight. This group has a unique irreducible, symplectic representation. Furthermore ...
Minh Van Tran, 1996
9
Quaternions and Rotation Sequences: A Primer with ...
It might be argued that since the tracking transformation involves only two rotations, and if these two tracking angles are the conventional tracking heading and the tracking elevation, then the di component of the tracking error-quaternion may ...
Jack B. Kuipers, 2002
10
Essentials of Managed Health Care
Value Shift The most significant struggle the military managed care system has grappled with from the inception of TRICARE to the present is the careful balance between elements of Coppola's Managed Care Quaternion (MCQ)24 and ...
Peter Reid Kongstvedt, 2007

10 NEWS ITEMS WHICH INCLUDE THE TERM «QUATERNION»

Find out what the national and international press are talking about and how the term quaternion is used in the context of the following news items.
1
orthonormal rotation and a quaternion bijection?
Well, you need to look at the trace of the matrix when going from matrix to quaternion, and there's an invsqrt in there. If that equals zero then you are in big ... «GameDev.net, Jun 15»
2
Creating a Quaternion from a direction
I can calculate the direction the ship needs to go from the ship position and target position, however a Vector is ofc not enough since I need a Quaternion to ... «GameDev.net, Jun 15»
3
Quaternion slerp: is this correct result?
But when I slerp q0->q1 to a value between 0 and 1, the resulting quaternion has the right axis, but the angle of the rotation is not enough to bring the point all ... «GameDev.net, May 15»
4
Quaternion Risk Management powers the InCol Analytics Platform …
Quaternion Risk Management Limited (“Quaternion”), provider of specialised risk analytics' consultancy, services and software, is now powering InCol. «Bobsguide, Mar 15»
5
finding delta quaternion to get from quat 'A' to quat 'B'
I'm working on trying to find a quaternion I can use that is a fraction of the difference between a starting quaternion, 'A', and a destination quaternion 'B'. I am not ... «GameDev.net, Mar 15»
6
Simple question on rotation matrix and quaternions
Given a SO(3) matrix, which should equivalently produce a unit quaternion ( with the real part positive ), I cannot successfully convert the matrix to a quaternion ... «GameDev.net, Feb 15»
7
Quaternion-UBS Delta Collaborate on CVA Front
Quaternion Risk Management, the Dublin-based provider of risk management technology and services, and UBS Delta have entered an alliance to provide ... «www.waterstechnology.com, Nov 14»
8
[SOLVED] Quaternion from direction not accurate
I used a look-at matrix and converted it to quaternion to have my look-at function but I wanted to change it to use quaternion directly. Here the actual code of the ... «GameDev.net, Nov 14»
9
Quaternion camera flipping constantly
It looks like there are 3 different rotation matrices being generated from the quaternion, one is actually correct and the other two are flipped or black, ... «GameDev.net, Oct 14»
10
Matrix to Quaternion calculation instable
Matrix to Quaternion calculation instable. Started by RPTD, Jul 13 2014 06:55 AM. quaterion matrix. Old topic! Google, the last post of this topic is over 60 days ... «GameDev.net, Jul 14»

REFERENCE
« EDUCALINGO. Quaternion [online]. Available <https://educalingo.com/en/dic-en/quaternion>. May 2024 ».
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