Definitions for Quaternion
kwəˈtɜr ni ənquater·nion

Princeton's WordNetRate this definition:0.0 / 0 votes

1. four, 4, IV, tetrad, quatern, quaternion, quaternary, quaternity, quartet, quadruplet, foursome, Little Joenoun

   the cardinal number that is the sum of three and one

WiktionaryRate this definition:5.0 / 1 vote

1. quaternionnoun

   A group or set of four people or things.

2. quaternionnoun

   A four-dimensional hypercomplex number that consists of a real dimension and 3 imaginary ones (i, j, k) that are each a square root of -1. They are commonly used in vector mathematics and in calculating the rotation of three-dimensional objects.

Samuel Johnson's DictionaryRate this definition:0.0 / 0 votes

1. Quaternionnoun

   The number four.

   Etymology: quaternio, Lat.

   Air and the elements! the eldest birth
   Of nature’s womb, that in quaternion run
   Perpetual circle, multiform; and mix
   And nourish all things; let your ceaseless change
   Vary to our great maker still new praise. John Milton.

   I have not in this scheme of these nine quaternions of consonants, distinct known characters, whereby to express them, but must repeat the same. William Holder, Elements of Speech.

WikipediaRate this definition:0.0 / 0 votes

1. Quaternion

   In mathematics, the quaternion number system extends the complex numbers. Quaternions were first described by the Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. Hamilton defined a quaternion as the quotient of two directed lines in a three-dimensional space, or, equivalently, as the quotient of two vectors. Multiplication of quaternions is noncommutative. Quaternions are generally represented in the form where a, b, c, and d are real numbers; and 1, i, j, and k are the basis vectors or basis elements.Quaternions are used in pure mathematics, but also have practical uses in applied mathematics, particularly for calculations involving three-dimensional rotations, such as in three-dimensional computer graphics, computer vision, and crystallographic texture analysis. They can be used alongside other methods of rotation, 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 a ring, being both a division ring and a domain. The algebra of quaternions is often denoted by H (for Hamilton), or in blackboard bold by H . {\displaystyle \mathbb {H} .} It can also be given by the Clifford algebra classifications Cl 0 , 2 ⁡ ( R ) ≅ Cl 3 , 0 + ⁡ ( R ) . {\displaystyle \operatorname {Cl} _{0,2}(\mathbb {R} )\cong \operatorname {Cl} _{3,0}^{+}(\mathbb {R} ).} In fact, it was the first noncommutative division algebra to be discovered. According to the Frobenius theorem, the algebra H {\displaystyle \mathbb {H} } is one of only two finite-dimensional division rings containing a proper subring isomorphic to the real numbers; the other being the complex numbers. These rings are also Euclidean Hurwitz algebras, of which the quaternions are the largest associative algebra (and hence the largest ring). Further extending the quaternions yields the non-associative octonions, which is the last normed division algebra over the real numbers. (The sedenions, the extension of the octonions, have zero divisors and so cannot be a normed division algebra.)The unit quaternions can be thought of as a choice of a group structure on the 3-sphere S3 that gives the group Spin(3), which is isomorphic to SU(2) and also to the universal cover of SO(3).

ChatGPTRate this definition:0.0 / 0 votes

1. quaternion

   A quaternion is a type of mathematical concept based in four dimensions. It consists of a real component and three imaginary components and is often used in calculations concerning three-dimensional rotations, such as those in computer graphics and aerospace navigation. It was invented by Irish mathematician Sir William Rowan Hamilton in 1843.

Webster DictionaryRate this definition:0.0 / 0 votes

1. Quaternionnoun

   the number four

2. Quaternionnoun

   a set of four parts, things, or person; four things taken collectively; a group of four words, phrases, circumstances, facts, or the like

3. Quaternionnoun

   a word of four syllables; a quadrisyllable

4. Quaternionnoun

   the quotient of two vectors, or of two directed right lines in space, considered as depending on four geometrical elements, and as expressible by an algebraic symbol of quadrinomial form

5. Quaternionverb

   to divide into quaternions, files, or companies

6. Etymology: [L. quaternio, fr. quaterni four each. See Quaternary.]

WikidataRate this definition:0.0 / 0 votes

1. 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 the product 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 can also be represented as the sum of a scalar and a vector. 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. 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 thus also form 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 . It can also be given by the Clifford algebra classifications Cℓ0,2 ≅ Cℓ03,0. The algebra H holds a special place in analysis since, according to the Frobenius theorem, it is one of only two finite-dimensional division rings containing the real numbers as a proper subring, the other being the complex numbers.³

Matched Categories

1. • Digit

How to pronounce Quaternion?

1. Alex

   US English

   David

   US English

   Mark

   US English

   Daniel

   British

   Libby

   British

   Mia

   British

   Karen

   Australian

   Hayley

   Australian

   Natasha

   Australian

   Veena

   Indian

   Priya

   Indian

   Neerja

   Indian

   Zira

   US English

   Oliver

   British

   Wendy

   British

   Fred

   US English

   Tessa

   South African

How to say Quaternion in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of Quaternion in Chaldean Numerology is: 1

2. Pythagorean Numerology

   The numerical value of Quaternion in Pythagorean Numerology is: 8

Popularity rank by frequency of use

References

1. ^ Princeton's WordNet
   http://wordnetweb.princeton.edu/perl/webwn?s=Quaternion
2. ^ Wiktionary
   https://en.wiktionary.org/wiki/Quaternion
3. ^ Samuel Johnson's Dictionary
   https://johnsonsdictionaryonline.com/views/search.php?term=Quaternion
4. ^ Wikipedia
   https://en.wikipedia.org/wiki/Quaternion
5. ^ ChatGPT
   https://chat.openai.com
6. ^ Webster Dictionary
   https://www.merriam-webster.com/dictionary/Quaternion
7. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=Quaternion