Editing Quaternion (section)

==Further reading==
===Books and publications===
{{refbegin|30em}}
*{{cite book |last=Adler |first=Stephen L. |title=Quaternionic quantum mechanics and quantum fields |publisher=Oxford University Press |year=1995 |isbn=0-19-506643-X |lccn=94006306 |series=International series of monographs on physics  |volume=88|ref=none }}
*{{cite journal |first=Simon L. |last=Altmann |title=Hamilton, Rodrigues, and the Quaternion Scandal |journal=Mathematics Magazine |volume=62 |issue=5 |pages=291–308 |year=1989 |doi=10.1080/0025570X.1989.11977459 |ref=none }}
*{{cite book |last1=Binz |first1=Ernst |first2=Sonja |last2=Pods |chapter=1. The Skew Field of Quaternions |title=Geometry of Heisenberg Groups |publisher=[[American Mathematical Society]] |year=2008 |isbn=978-0-8218-4495-3 |ref=none }}
*{{cite EB1911|wstitle=Algebra|ref=none }} (''See section on quaternions.'')
*{{cite book |last=Clerk Maxwell |first=James |author-link=James Clerk Maxwell |year=1873 |title=[[A Treatise on Electricity and Magnetism]] |publisher=Clarendon Press |location=Oxford |ref=none}}
*{{cite book |last1=Conway |first1=John Horton |author-link=John Horton Conway |last2=Smith |first2=Derek A. |title=On Quaternions and Octonions: Their Geometry, Arithmetic, and Symmetry |publisher=A.K. Peters |year=2003 |isbn=1-56881-134-9 }} ([http://nugae.wordpress.com/2007/04/25/on-quaternions-and-octonions/ review]).
*{{cite book |last=Crowe |first=Michael J. |year=1967 |title=[[A History of Vector Analysis]]: The Evolution of the Idea of a Vectorial System |publisher=University of Notre Dame Press |ref=none}} Surveys the major and minor vector systems of the 19th century (Hamilton, Möbius, Bellavitis, Clifford, Grassmann, Tait, Peirce, Maxwell, Macfarlane, MacAuley, Gibbs, Heaviside).
*{{cite book |last1=Doran |first1=Chris J.L. |first2=Anthony N. |last2=Lasenby |title=Geometric Algebra for Physicists |year=2003 |publisher=Cambridge University Press |isbn=978-0-521-48022-2 |author1-link=Chris J. L. Doran|ref=none }}
*{{cite book |last=Du Val |first=Patrick |author-link=Patrick du Val |title=Homographies, quaternions, and rotations |publisher=Clarendon Press |series=Oxford mathematical monographs |year=1964 |lccn=64056979|ref=none }}
*{{cite journal |last=Evans |first=D.J. |title=On the Representation of Orientation Space |journal=Mol. Phys. |volume=34 |issue=2 |pages=317–325 |year=1977 |doi=10.1080/00268977700101751 |bibcode=1977MolPh..34..317E |ref=none }} For molecules that can be regarded as classical rigid bodies, [[molecular dynamics]] computer simulation employs quaternions.
*{{ cite book |last1=Eves |first1=Howard |title=An Introduction to the History of Mathematics |edition=4th | location=New York |publisher=Holt, Rinehart and Winston |year=1976 |isbn=0-03-089539-1 }}
*{{cite journal |last1=Finkelstein |first1=David |first2=Josef M. |last2=Jauch |first3=Samuel |last3=Schiminovich |first4=David |last4=Speiser |title=Foundations of quaternion quantum mechanics |journal=J. Math. Phys. |volume=3 |pages=207–220 |year=1962 |issue=2 |doi=10.1063/1.1703794 |bibcode=1962JMP.....3..207F |s2cid=121453456 |url=https://archive-ouverte.unige.ch/unige:162173 |ref=none }}
*{{cite journal |first=Fuzhen |last=Zhang |title=Quaternions and Matrices of Quaternions |journal=Linear Algebra and Its Applications |volume=251 |pages=21–57 |year=1997 |doi=10.1016/0024-3795(95)00543-9 |doi-access=free |ref=none }}
*{{cite book |last=Goldman |first=Ron |title=Rethinking Quaternions: Theory and Computation|year=2010|publisher=Morgan & Claypool |isbn=978-1-60845-420-4|ref=none }}
*{{cite book |last1=Gürlebeck |first1=Klaus |last2=Sprössig |first2=Wolfgang |title=Quaternionic and Clifford calculus for physicists and engineers |publisher=Wiley |year=1997 |isbn=0-471-96200-7 |series=Mathematical methods in practice |volume=1 |lccn=98169958|ref=none }}
*{{cite journal |author-link=William Rowan Hamilton |first=William Rowan |last=Hamilton |title=On quaternions, or on a new system of imaginaries in algebra |journal=Philosophical Magazine |volume=25 |issue=3 |pages=489–495 |year=1844 |doi=10.1080/14786444408645047 |url=https://zenodo.org/record/1431043 |ref=none }}
*[[William Rowan Hamilton|Hamilton, William Rowan]] (1853), "''[https://web.archive.org/web/20140808040037/http://www.ugcs.caltech.edu/~presto/papers/Quaternions-Britannica.ps.bz2 Lectures on Quaternions]''". Royal Irish Academy.
*Hamilton (1866) ''[https://archive.org/details/bub_gb_fIRAAAAAIAAJ Elements of Quaternions]'' [[University of Dublin]] Press. Edited by William Edwin Hamilton, son of the deceased author.
*Hamilton (1899) ''Elements of Quaternions'' volume I, (1901) volume II. Edited by [[Charles Jasper Joly]]; published by [[Longmans, Green & Co.]]
*{{cite book |last=Hanson |first=Andrew J. |title=Visualizing Quaternions |publisher=Elsevier |year=2006 |isbn=0-12-088400-3 |url=http://www.cs.indiana.edu/~hanson/quatvis/|ref=none }}
*{{cite book |last1=Hazewinkel |first1=Michiel |author-link=Michiel Hazewinkel |first2=Nadiya |last2=Gubareni |first3=Vladimir V. |last3=Kirichenko |title=Algebras, rings and modules |publisher=Springer |year=2004 |isbn=1-4020-2690-0 |volume=1 |url=https://books.google.com/books?id=AibpdVNkFDYC  }}
*{{cite arXiv |last=Jack |first=P.M. |title=Physical space as a quaternion structure, I: Maxwell equations. A brief Note |date=2003 |eprint=math-ph/0307038|ref=none }} 
*{{cite book |last=Joly |first=Charles Jasper |title=A manual of quaternions |publisher=Macmillan |year=1905 |lccn=05036137|ref=none }}
*{{cite book |last1=Kantor |first1=I.L. |last2=Solodnikov |first2=A.S. |title=Hypercomplex numbers, an elementary introduction to algebras |publisher=Springer-Verlag |year=1989 |isbn=0-387-96980-2 |ref=none }}
*{{cite book |last=Kravchenko |first=Vladislav |title=Applied Quaternionic Analysis |publisher=Heldermann Verlag |year=2003 |isbn=3-88538-228-8 |ref=none }}
*{{cite book |last=Kuipers |first=Jack |title=Quaternions and Rotation Sequences: A Primer With Applications to Orbits, Aerospace, and Virtual Reality |publisher=[[Princeton University Press]] |year=2002 |isbn=0-691-10298-8 |ref=none }}
*{{cite book |last=Macfarlane |first=Alexander |author-link=Alexander Macfarlane |title=Vector analysis and quaternions |publisher=Wiley |edition=4th |year=1906 |lccn=16000048|ref=none }}
*{{cite journal |last=Pujol |first=Jose |title=On Hamilton's Nearly-Forgotten Early Work on the Relation between Rotations and Quaternions and on the Composition of Rotations |journal=The American Mathematical Monthly |volume=121 |issue=6 |pages=515–522 |year=2014 |doi=10.4169/amer.math.monthly.121.06.515 |s2cid=1543951 |ref=none }}
*{{cite book |last=Tait |first=Peter Guthrie |author-link=Peter Guthrie Tait |year=1873|title=An elementary treatise on quaternions |edition=2nd |location=Cambridge |publisher=The University Press |ref=none}}
*{{cite book |last=Vince |first=John A. |title=Geometric Algebra for Computer Graphics |publisher=Springer |year=2008 |isbn=978-1-84628-996-5 |ref=none }}
*{{cite book |last=Voight |first=John |title=Quaternion Algebras |series=Graduate Texts in Mathematics |publisher=Springer |year=2021 |volume=288 |isbn=978-3-030-57467-3 |doi=10.1007/978-3-030-56694-4 |doi-access=free |ref=none }}
*{{cite book |last=Ward |first=J.P. |title=Quaternions and Cayley Numbers: Algebra and Applications |publisher=Kluwer Academic |year=1997 |isbn=0-7923-4513-4 |ref=none }}
{{refend}}

===Links and monographs===
{{refbegin|30em}}
* {{cite web |title=Quaternion Notices |url=https://quaternionnews.commons.gc.cuny.edu/ }} Notices and materials related to Quaternion conference presentations
* {{springer|title=Quaternion|id=p/q076770}}
* {{cite web |title=Frequently Asked Questions |work=Matrix and Quaternion  |id=1.21 |url=http://www.j3d.org/matrix_faq/matrfaq_latest.html|ref=none}}
* {{cite web |first=Doug |last=Sweetser |title=Doing Physics with Quaternions |url=http://world.std.com/~sweetser/quaternions/qindex/qindex.html |ref=none }}
* [https://web.archive.org/web/20050408193941/http://www.fho-emden.de/~hoffmann/quater12012002.pdf Quaternions for Computer Graphics and Mechanics (Gernot Hoffman)]
* {{cite arXiv |title=The Physical Heritage of Sir W. R. Hamilton |eprint=math-ph/0201058|last1=Gsponer|first1=Andre|last2=Hurni|first2=Jean-Pierre|year=2002|ref=none }}
* {{cite web |first=D.R. |last=Wilkins |title=Hamilton's Research on Quaternions |url=http://www.maths.tcd.ie/pub/HistMath/People/Hamilton/Quaternions.html |ref=none }}
* {{cite web |first=David J. |last=Grossman |title=Quaternion Julia Fractals |url=http://www.unpronounceable.com/julia/ |ref=none }} 3D Raytraced Quaternion [[Julia set|Julia Fractals]]
* {{cite web |title=Quaternion Math and Conversions |url=http://www.euclideanspace.com/maths/algebra/realNormedAlgebra/quaternions/index.htm|ref=none }} Great page explaining basic math with links to straight forward rotation conversion formulae.
* {{cite web |first=John H. |last=Mathews |title=Bibliography for Quaternions |url=http://math.fullerton.edu/mathews/c2003/QuaternionBib/Links/QuaternionBib_lnk_3.html|archive-url=https://web.archive.org/web/20060902200454/http://math.fullerton.edu/mathews/c2003/QuaternionBib/Links/QuaternionBib_lnk_3.html |archive-date=2006-09-02 |ref=none }} 
* {{cite web |title=Quaternion powers |publisher=GameDev.net |url=https://www.gamedev.net/articles/programming/math-and-physics/quaternion-powers-r1095/|ref=none }}
* {{cite web |first=Andrew |last=Hanson |title=Visualizing Quaternions home page |url=http://books.elsevier.com/companions/0120884003/vq/index.html |archive-url=https://web.archive.org/web/20061105174313/http://books.elsevier.com/companions/0120884003/vq/index.html |archive-date=2006-11-05 |ref=none }}
* {{cite journal |first=Charles F.F. |last=Karney |title=Quaternions in molecular modeling |journal=J. Mol. Graph. Mod. |volume=25 |issue=5 |pages=595–604 |date=January 2007 |doi=10.1016/j.jmgm.2006.04.002 |pmid=16777449 |arxiv=physics/0506177|bibcode=2007JMGM...25..595K |s2cid=6690718 |ref=none }}
* {{cite arXiv |first=Johan E. |last=Mebius |title=A matrix-based proof of the quaternion representation theorem for four-dimensional rotations |year=2005 |eprint=math/0501249|ref=none }}
* {{cite arXiv |first=Johan E. |last=Mebius |title=Derivation of the Euler–Rodrigues formula for three-dimensional rotations from the general formula for four-dimensional rotations |year=2007 |eprint=math/0701759|ref=none }}  
* {{cite web |title=Hamilton Walk |publisher=Department of Mathematics, [[NUI Maynooth]] |url=http://www.maths.nuim.ie/links/hamilton.shtml|ref=none }}
* {{cite web |title=Using Quaternions to represent rotation |work=OpenGL:Tutorials |url=http://gpwiki.org/index.php/OpenGL:Tutorials:Using_Quaternions_to_represent_rotation |archive-url=https://web.archive.org/web/20071215235040/http://gpwiki.org/index.php/OpenGL:Tutorials:Using_Quaternions_to_represent_rotation |archive-date=2007-12-15 |ref=none }}
* David Erickson, [[Defence Research and Development Canada]] (DRDC), Complete derivation of rotation matrix from unitary quaternion representation in DRDC TR 2005-228 paper. 
* {{cite web |first=Alberto |last=Martinez |title=Negative Math, How Mathematical Rules Can Be Positively Bent |publisher=Department of History, University of Texas |url=https://webspace.utexas.edu/aam829/1/m/NegativeMath.html|archive-url=https://web.archive.org/web/20110924161347/https://webspace.utexas.edu/aam829/1/m/NegativeMath.html |archive-date=2011-09-24 |ref=none }}
* {{cite web |first=D. |last=Stahlke |title=Quaternions in Classical Mechanics |url=http://www.stahlke.org/dan/phys-papers/quaternion-paper.pdf|ref=none }}
* {{cite arXiv |last1=Morier-Genoud |first1=Sophie |first2=Valentin |last2=Ovsienko |title=Well, Papa, can you multiply triplets? |year=2008 |class=math.AC |eprint=0810.5562|ref=none }} describes how the quaternions can be made into a skew-commutative algebra graded by {{nowrap|'''Z'''/2 × '''Z'''/2 × '''Z'''/2}}.
* {{cite web |first=Helen |last=Joyce |title=Curious Quaternions |date=November 2004 |publisher=hosted by [[John Baez]] |url=http://plus.maths.org/content/os/issue32/features/baez/index|ref=none }}
* {{cite web |first=Luis |last=Ibanez |title=Tutorial on Quaternions. Part I |url=http://www.itk.org/CourseWare/Training/QuaternionsI.pdf |access-date=2011-12-05 |archive-url=https://web.archive.org/web/20120204055438/http://www.itk.org/CourseWare/Training/QuaternionsI.pdf |archive-date=2012-02-04 |url-status=dead |ref=none }} [https://web.archive.org/web/20121005003247/http://www.itk.org/CourseWare/Training/QuaternionsII.pdf Part II] (PDF; using Hamilton's terminology, which differs from the modern usage)
* {{cite journal |first1=R. |last1=Ghiloni |first2=V. |last2=Moretti |first3=A. |last3=Perotti |title=Continuous slice functional calculus in quaternionic Hilbert spaces |journal=Rev. Math. Phys. |volume=25 |pages=1350006–126 |year=2013 |issue=4 |doi=10.1142/S0129055X13500062 |arxiv=1207.0666|bibcode=2013RvMaP..2550006G |s2cid=119651315 |ref=none }}<br />{{cite journal |first1=R. |last1=Ghiloni |first2=V. |last2=Moretti |first3=A. |last3=Perotti |title=Spectral representations of normal operators via Intertwining Quaternionic Projection Valued Measures |journal=Rev. Math. Phys. |volume=29 |pages=1750034 |year=2017 |doi=10.1142/S0129055X17500349 |arxiv=1602.02661|s2cid=124709652 |ref=none }} two expository papers about continuous functional calculus and spectral theory in quanternionic Hilbert spaces useful in rigorous quaternionic quantum mechanics.
* [https://play.google.com/store/apps/details?id=com.MoritzWillProduction.Quaternions Quaternions] the Android app shows the quaternion corresponding to the orientation of the device.
* [https://www.gamedeveloper.com/programming/rotating-objects-using-quaternions Rotating Objects Using Quaternions] article speaking to the use of Quaternions for rotation in video games/computer graphics.
{{refend}}