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• Quaternion abstract "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 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 (for Hamilton), or in blackboard bold by (Unicode U+210D, ℍ). It can also be given by the Clifford algebra classifications Cℓ0,2(R) ≅ Cℓ03,0(R). 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. These rings are also Euclidean Hurwitz algebras, of which quaternions are the largest associative algebra.The unit quaternions can therefore 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).".
• Quaternion thumbnail Quaternion2.png?width=300.
• Quaternion wikiPageExternalLink attitude.html.
• Quaternion wikiPageExternalLink quaternion.pdf.
• Quaternion wikiPageExternalLink 0810.5562.
• Quaternion wikiPageExternalLink 0501249.
• Quaternion wikiPageExternalLink 0701759.
• Quaternion wikiPageExternalLink 0506177.
• Quaternion wikiPageExternalLink 1207.0666.pdf.
• Quaternion wikiPageExternalLink 0201058.
• Quaternion wikiPageExternalLink index.html.
• Quaternion wikiPageExternalLink books?id=fIRAAAAAIAAJ.
• Quaternion wikiPageExternalLink OpenGL:Tutorials:Using_Quaternions_to_represent_rotation.
• Quaternion wikiPageExternalLink docviewer?did=05230001&seq=9.
• Quaternion wikiPageExternalLink QuaternionBib_lnk_3.html.
• Quaternion wikiPageExternalLink vtrifonov.
• Quaternion wikiPageExternalLink on-quaternions-and-octonions.
• Quaternion wikiPageExternalLink index.
• Quaternion wikiPageExternalLink qindex.html.
• Quaternion wikiPageExternalLink Quaternions.
• Quaternion wikiPageExternalLink quatvis.
• Quaternion wikiPageExternalLink OnQuat.pdf.
• Quaternion wikiPageExternalLink index.htm.
• Quaternion wikiPageExternalLink quater12012002.pdf.
• Quaternion wikiPageExternalLink article1095.asp.
• Quaternion wikiPageExternalLink Documentation.html.
• Quaternion wikiPageExternalLink DocumentationBody.html.
• Quaternion wikiPageExternalLink Mathematics.html.
• Quaternion wikiPageExternalLink MathematicsBody.html.
• Quaternion wikiPageExternalLink QuaternionsI.pdf.
• Quaternion wikiPageExternalLink QuaternionsII.pdf.
• Quaternion wikiPageExternalLink matrfaq_latest.html.
• Quaternion wikiPageExternalLink hamilton.shtml.
• Quaternion wikiPageExternalLink Quaternions.html.
• Quaternion wikiPageExternalLink quaternion-paper.pdf.
• Quaternion wikiPageExternalLink Quaternions-Britannica.ps.bz2.
• Quaternion wikiPageExternalLink julia.
• Quaternion wikiPageExternalLink english.
• Quaternion wikiPageExternalLink NegativeMath.html.
• Quaternion wikiPageID "51440".
• Quaternion wikiPageRevisionID "602896036".
• Quaternion hasPhotoCollection Quaternion.
• Quaternion id "p/q076770".
• Quaternion title "Quaternion".
• Quaternion subject Category:Quaternions.
• Quaternion comment "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.".
• Quaternion label "Cuaternión".
• Quaternion label "Kwaterniony".
• Quaternion label "Quaternion".
• Quaternion label "Quaternion".
• Quaternion label "Quaternion".
• Quaternion label "Quaternion".
• Quaternion label "Quaternione".
• Quaternion label "Quaterniões".
• Quaternion label "Кватернион".
• Quaternion label "كواتيرنيون".
• Quaternion label "四元数".
• Quaternion label "四元數".
• Quaternion sameAs Kvaternion.
• Quaternion sameAs Quaternion.
• Quaternion sameAs Τετραδόνιο.
• Quaternion sameAs Cuaternión.
• Quaternion sameAs Koaternioi.
• Quaternion sameAs Quaternion.
• Quaternion sameAs Kuaternion.
• Quaternion sameAs Quaternione.
• Quaternion sameAs 四元数.
• Quaternion sameAs 사원수.
• Quaternion sameAs Quaternion.
• Quaternion sameAs Kwaterniony.
• Quaternion sameAs Quaterniões.
• Quaternion sameAs m.0dkqr.
• Quaternion sameAs Q173853.
• Quaternion sameAs Q173853.
• Quaternion wasDerivedFrom Quaternion?oldid=602896036.
• Quaternion depiction Quaternion2.png.
• Quaternion isPrimaryTopicOf Quaternion.