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Explore Quaternion through 10+ example sentences from English, with an explanation of the meaning and related words like four or digit. Ideal for language learners, writers and word enthusiasts.

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Quaternion in a sentence

Related words

Quaternion | Quaternions | Quaternionic

Quaternion meaning

  1. A group or set of four people or things.
  2. A word of four syllables.
  3. A type of four-dimensional hypercomplex number consisting of a real part and three imaginary parts (real multiples of distinct, independent square roots of −1 denoted by i, j and k); commonly used in vector mathematics and as an alternative to matrix algebra in calculating the rotation of three-dimensional objects.

Synonyms of Quaternion

four digit little joe foursome quadruplet quartet quaternity quaternary quatern tetrad iv 4 figure

Related words

Other words often associated with Quaternion or its synonyms:

cardinal quartette shape gathering fourth integer appendage fig anatomy period amount soma

Using Quaternion

  • The main meaning on this page is: A group or set of four people or things. | A word of four syllables. | A type of four-dimensional hypercomplex number consisting of a real part and three imaginary parts (real multiples of distinct, independent square roots of −1 denoted by i, j and k); commonly used in vector mathematics and as an alternative to matrix algebra in calculating the rotation of three-dimensional objects.
  • Useful related words include: four, digit, little joe, foursome.
  • In the example corpus, quaternion often appears in combinations such as: of quaternion, quaternion can, by quaternion.

Context around Quaternion

  • Average sentence length in these examples: 26.1 words
  • Position in the sentence: 8 start, 7 middle, 5 end
  • Sentence types: 20 statements, 0 questions, 0 exclamations

Often before:

imaginary 2× unit 2× complete 1× pure 1× holy 1× quaternions 1× mathematical 1× theorem 1× combining 1×

Often after:

similarity 1× representation 1× representations 1× study 1× product 1× variable 1× squares 1× multiplication 1× algebra 1× plaque 1×

Sentence patterns with Quaternion

These short patterns come directly from the example sentences and show how the word is often embedded:

a pure quaternion 1× a quaternion representation of 1× a unit quaternion a quaternion 1× a unit quaternion and with 1× as a quaternion 1× by a quaternion similarity transform 1× complication with quaternion representations of 1× given by quaternion multiplication see 1×

Sentence openings and endings

Common sentence openings:

a polar vector 1× a quaternion representation 1× clifford simplified the 1× conjugation by a 1× even though every 1× first then must 1×

Common sentence endings:

a pure quaternion 1× a quaternion variable 1× always pure imaginary 1× as a quaternion 1× complete quaternion product 1× many matrix transformations 1×

Words around Quaternion

Just before it in the word index:

quaternary 64 quaterfinals 2 quat 3 quasten 2 quastel 2 quast 3

Just after it in the word index:

quaternionic 3 quaternions 51 quatford 2 quatloo 2 quatrain 13 quatrains 18

Similar in corpus frequency:

abattoirs 31 aberrant 31 abike 31 ablative 31 abloh 31 absurdities 31

Corpus analysis for Quaternion

  • In this selection, "quaternion" usually appears near the start of the sentence. The average example has 26.1 words, and this corpus slice is mostly made up of statements.
  • Around the word, imaginary, unit, complete, similarity, representation and representations stand out and add context to how "quaternion" is used.
  • Recognizable usage signals include a pure quaternion and a quaternion representation of. That gives this page its own corpus information beyond isolated example sentences.
  • By corpus frequency, "quaternion" sits close to words such as abattoirs, aberrant and abike, which helps place it inside the broader word index.

Example types with quaternion

The same corpus examples are grouped by length and sentence type, making it easier to see the contexts in which the word appears:

Short example sentences

Then we may state : :Stone–Weierstrass Theorem (quaternion numbers). (9 words)

See polar decomposition of a quaternion for details of this development of the three-sphere. (15 words)

The rationale is that combining quaternion transformations is more numerically stable than combining many matrix transformations. (16 words)

Longer example sentences

Perwass also claims here that David Hestenes coined the term "versor", where he is presumably is referring to the GA context (the term versor appears to have been used by Hamilton to refer to an equivalent object of the quaternion algebra). (41 words)

The mathematical quaternion partakes of both these elements; in technical language it may be said to be 'time plus space', or 'space plus time': and in this sense it has, or at least involves a reference to, four dimensions. (39 words)

Notice that replacing i by −i, j by −j, and k by −k sends a vector to its additive inverse, so the additive inverse of a vector is the same as its conjugate as a quaternion. (36 words)

Example sentences (20)

A polar vector can be represented in calculations (for example, when rotated by a quaternion "similarity transform") by a pure imaginary quaternion, with no loss of information, but the two should not be confused.

A quaternion representation of the fermions might be: : A further complication with quaternion representations of fermions is that there are two types of multiplication: left multiplication and right multiplication which must be taken into account.

Clifford simplified the quaternion study by isolating the dot product and cross product of two vectors from the complete quaternion product.

Conjugation by a unit quaternion (a quaternion of absolute value 1) with real part cos(θ) is a rotation by an angle 2θ, the axis of the rotation being the direction of the imaginary part.

Even though every quaternion can be viewed as a vector in a four-dimensional vector space, it is common to define a vector to mean a pure imaginary quaternion.

In the second equality above, we have identified with a unit quaternion and with a pure quaternion.

Unlike the situation in the complex plane, the conjugation of a quaternion can be expressed entirely with multiplication and addition: : Conjugation can be used to extract the scalar and vector parts of a quaternion.

First then must be put the holy quaternion of the gospels; following them the Acts of the Apostles..

Advertentie

For example, the original electric and magnetic fields described by Maxwell were functions of a quaternion variable.

In other words, a quaternion squares to −1 if and only if it is a vector (that is, pure imaginary) with norm 1. By definition, the set of all such vectors forms the unit sphere.

Much of the interesting geometry of the 3-sphere stems from the fact that the 3-sphere has a natural Lie group structure given by quaternion multiplication (see the section below on group structure).

Multiplying a quaternion by a real number scales its norm by the absolute value of the number.

Notice that replacing i by −i, j by −j, and k by −k sends a vector to its additive inverse, so the additive inverse of a vector is the same as its conjugate as a quaternion.

Perwass also claims here that David Hestenes coined the term "versor", where he is presumably is referring to the GA context (the term versor appears to have been used by Hamilton to refer to an equivalent object of the quaternion algebra).

Quaternions Quaternion Plaque on Broom Bridge The other great contribution Hamilton made to mathematical science was his discovery of quaternions in 1843.

See polar decomposition of a quaternion for details of this development of the three-sphere.

The mathematical quaternion partakes of both these elements; in technical language it may be said to be 'time plus space', or 'space plus time': and in this sense it has, or at least involves a reference to, four dimensions.

Then we may state : :Stone–Weierstrass Theorem (quaternion numbers).

The rationale is that combining quaternion transformations is more numerically stable than combining many matrix transformations.

The scalar part of a quaternion is always real, and the vector part is always pure imaginary.

Advertentie

Common combinations with quaternion

These word pairs occur most frequently in English texts:

Frequently asked questions

How do you use "quaternion" in a sentence?
An example: "A polar vector can be represented in calculations (for example, when rotated by a quaternion "similarity transform") by a pure imaginary quaternion, with no loss of information, but the two should not be confused." This page contains 10+ example sentences with the word "quaternion" from authentic English texts.
What does "quaternion" mean?
Quaternion means: A group or set of four people or things.
What are synonyms of "quaternion"?
Common synonyms of "quaternion" include: four, digit, little joe, foursome, quadruplet, quartet, quaternity, quaternary. Plus 5 more synonyms.
How many example sentences with "quaternion" are there?
Voorbeeldzinnen.info contains at least 10+ example sentences with "quaternion", drawn from a database of millions of English sentences.