Quaternion (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Quaternion" in English language version.

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16doi.org

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ams.org (Global: 451^st place; English: 277^th place)

mathscinet.ams.org

Porteous, Ian R. (1995). "Chapter 8: Quaternions". Clifford Algebras and the Classical Groups (PDF). Cambridge Studies in Advanced Mathematics. Vol. 50. Cambridge: Cambridge University Press. p. 60. doi:10.1017/CBO9780511470912.009. ISBN 9780521551779. MR 1369094. OCLC 32348823.

archive.org (Global: 6^th place; English: 6^th place)

Hamilton described quaternions in a letter to John Graves, 17 October 1843. It was published in Hamilton (1844). Hamilton, William Rowan (1844). "On Quaternions; or on a new System of Imaginaries in Algebra". Philosophical Magazine. Ser. 3. 25 supplement (169): 489–495. doi:10.1080/14786444408645047.
Hamilton, W.R., Sir (1853). Lectures on Quaternions. Dublin, EI: Hodges & Smith. p. 60. quaternion quotient lines tridimensional space time{{cite book}}: CS1 maint: multiple names: authors list (link)
Hamilton, W.R., Sir (1866). Hamilton, W.E. (ed.). Elements of Quaternions. London: Longmans, Green, & Co.{{cite book}}: CS1 maint: multiple names: authors list (link)
Ludwik Silberstein (1914) The Theory of Relativity via Internet Archive
Hamilton, W.R., Sir (1866). "Article 285". Elements of Quaternions. Longmans, Green, & Company. p. 310.{{cite book}}: CS1 maint: multiple names: authors list (link)
Gibbs, J. Willard; Wilson, Edwin Bidwell (1901). Vector Analysis. Yale University Press. p. 428. right tensor dyadic
Perlis, Sam (1971). "Capsule 77: Quaternions". Historical Topics in Algebra. Historical Topics for the Mathematical Classroom. Vol. 31. Reston, VA: National Council of Teachers of Mathematics. p. 39. ISBN 9780873530583. OCLC 195566.
Hamilton, W.R. (1853). Lectures on Quaternions. Dublin, IE: Hodges & Smith. p. 522.
Graves, R.P. Life of Sir William Rowan Hamilton. Dublin Hodges, Figgis. pp. 635–636.
Thompson, Silvanus Phillips (1910). The life of William Thomson. Vol. 2. London, UK: Macmillan. p. 1138.
Heaviside, Oliver (1893). Electromagnetic Theory. Vol. I. London, UK: The Electrician Printing and Publishing Company. pp. 134–135.
Silberstein, Ludwik (1924). "Preface to second edition". The Theory of Relativity (2nd ed.).

arxiv.org (Global: 69^th place; English: 59^th place)

Hanson, Jason (2011). "Rotations in three, four, and five dimensions". arXiv:1103.5263 [math.MG].

books.google.com (Global: 3^rd place; English: 3^rd place)

Rozenfelʹd, Boris Abramovich (1988). The history of non-euclidean geometry: Evolution of the concept of a geometric space. Springer. p. 385. ISBN 9780387964584.
Hardy, A.S. (1881). Elements of Quaternions. Vol. 2. Ginn, Heath, & Co. p. 32. doi:10.1126/science.os-2.75.564. ISBN 9781429701860. PMID 17819877. {{cite book}}: ISBN / Date incompatibility (help); |journal= ignored (help)
See Hazewinkel, Gubareni & Kirichenko 2004, p. 12 Hazewinkel, Michiel; Gubareni, Nadiya; Kirichenko, Vladimir V. (2004). Algebras, rings and modules. Vol. 1. Springer. ISBN 1-4020-2690-0.
Conway & Smith 2003, p. 9 Conway, John Horton; Smith, Derek A. (2003). On Quaternions and Octonions: Their Geometry, Arithmetic, and Symmetry. A.K. Peters. ISBN 1-56881-134-9. (review).
Bradley, Robert E.; Sandifer, Charles Edward (2007). Leonhard Euler: Life, work and legacy. Elsevier. p. 193. ISBN 978-0-444-52728-8.
Gauss, C.F. (c. 1819). "Mutationen des Raumes" [Transformations of space]. In Martin Brendel (ed.). Carl Friedrich Gauss Werke [The works of Carl Friedrich Gauss]. Vol. 8. Prof. Stäckel of Kiel, Germany (article edited by). Göttingen, DE: Königlichen Gesellschaft der Wissenschaften [Royal Society of Sciences] (published 1900). pp. 357–361 – via Google.
McCarthy, J.M. (1990). An Introduction to Theoretical Kinematics. MIT Press. ISBN 978-0-262-13252-7.

bridgesmathart.org (Global: low place; English: low place)

archive.bridgesmathart.org

"[no title cited]" (PDF). bridgesmathart.org. archive. Retrieved 19 August 2018.

cmu.edu (Global: 1,564^th place; English: 1,028^th place)

cs.cmu.edu

Shoemake, Ken (1985). "Animating rotation with quaternion curves" (PDF). Computer Graphics. 19 (3): 245–254. doi:10.1145/325165.325242. Presented at SIGGRAPH '85.

cornell.edu (Global: 332^nd place; English: 246^th place)

classe.cornell.edu

"Three-Dimensional Point Groups". www.classe.cornell.edu. Retrieved 2022-12-09.

diva-portal.org (Global: 3,588^th place; English: 3,072^nd place)

Günaşti, Gökmen (2016). Quaternions Algebra, Their Applications in Rotations and Beyond Quaternions (BS). Linnaeus University.

doi.org (Global: 2^nd place; English: 2^nd place)

Hamilton described quaternions in a letter to John Graves, 17 October 1843. It was published in Hamilton (1844). Hamilton, William Rowan (1844). "On Quaternions; or on a new System of Imaginaries in Algebra". Philosophical Magazine. Ser. 3. 25 supplement (169): 489–495. doi:10.1080/14786444408645047.
Hardy, A.S. (1881). Elements of Quaternions. Vol. 2. Ginn, Heath, & Co. p. 32. doi:10.1126/science.os-2.75.564. ISBN 9781429701860. PMID 17819877. {{cite book}}: ISBN / Date incompatibility (help); |journal= ignored (help)
Mamone, Salvatore; Pileio, Giuseppe; Levitt, Malcolm H. (2010). "Orientational Sampling Schemes Based on Four Dimensional Polytopes". Symmetry. 2 (3): 1423–1449. Bibcode:2010Symm....2.1423M. doi:10.3390/sym2031423.
Kunze, Karsten; Schaeben, Helmut (November 2004). "The Bingham distribution of quaternions and its spherical radon transform in texture analysis". Mathematical Geology. 36 (8): 917–943. Bibcode:2004MatGe..36..917K. doi:10.1023/B:MATG.0000048799.56445.59. S2CID 55009081.
Shoemake, Ken (1985). "Animating rotation with quaternion curves" (PDF). Computer Graphics. 19 (3): 245–254. doi:10.1145/325165.325242. Presented at SIGGRAPH '85.
Lambek, J. (1995). "If Hamilton had prevailed: Quaternions in physics". The Mathematical Intelligencer. Vol. 17, no. 4. pp. 7–15. doi:10.1007/BF03024783.
Clifford, W.K. (1878). "Applications of Grassmann's Extensive Algebra". American Journal of Mathematics. 1 (4). The Johns Hopkins University Press: 350–358. doi:10.2307/2369379. JSTOR 2369379./
Peirce, B. (1881). "Linear associative algebra". American Journal of Mathematics. 4 (1). Johns Hopkins University: 221–226. doi:10.2307/2369153.
Girard, P.R.; Clarysse, P.; Pujol, R.; Goutte, R.; Delachartre, P. (2018). "Hyperquaternions: a new tool for physics". Advances in Applied Clifford Algebras. 28. Springer: 1–14. doi:10.1007/s00006-018-0881-8.
Girard, P.R.; Clarysse, P.; Pujol, R.; Delachartre, P. (2025). "Hyperquaternionic unitary symplectic groups: A unifying tool for physics". Advances in Applied Clifford Algebras. 35 (40). Springer. doi:10.1007/s00006-025-01402-w.
Gürlebeck, K.; Habetha, K.; Sprössig, W. (2016). Application of holomorphic functions in two and higher dimensions. Springer.
Sprössig, W. (2020). "Some new aspects in hypercomplex analysis". Advancements in Complex Analysis: From Theory to Practice. Springer. pp. 497–518.
Hardy, A.S. (1881). Elements of Quaternions. Vol. 2. Ginn, Heath, & Co. p. 65 or 81 (?). doi:10.1126/science.os-2.75.564. ISBN 9781429701860. PMID 17819877. {{cite book}}: |journal= ignored (help)CS1 maint: ignored ISBN errors (link)
Farebrother, Richard William; Groß, Jürgen; Troschke, Sven-Oliver (2003). "Matrix representation of quaternions". Linear Algebra and Its Applications. 362: 251–255. doi:10.1016/s0024-3795(02)00535-9.
Porteous, Ian R. (1995). "Chapter 8: Quaternions". Clifford Algebras and the Classical Groups (PDF). Cambridge Studies in Advanced Mathematics. Vol. 50. Cambridge: Cambridge University Press. p. 60. doi:10.1017/CBO9780511470912.009. ISBN 9780521551779. MR 1369094. OCLC 32348823.
Park, F.C.; Ravani, Bahram (1997). "Smooth invariant interpolation of rotations". ACM Transactions on Graphics. 16 (3): 277–295. doi:10.1145/256157.256160. S2CID 6192031.

ed.ac.uk (Global: 1,871^st place; English: 1,234^th place)

maths.ed.ac.uk

Porteous, Ian R. (1995). "Chapter 8: Quaternions". Clifford Algebras and the Classical Groups (PDF). Cambridge Studies in Advanced Mathematics. Vol. 50. Cambridge: Cambridge University Press. p. 60. doi:10.1017/CBO9780511470912.009. ISBN 9780521551779. MR 1369094. OCLC 32348823.

gamedeveloper.com (Global: 4,881^st place; English: 2,796^th place)

Bobick, Nick (July 1998). "Rotating objects using quaternions". Game Developer.

geometricalgebra.net (Global: low place; English: low place)

"Quaternions and Geometric Algebra". geometricalgebra.net. Archived from the original on 2008-09-08. Retrieved 2008-09-12. See also: Dorst, Leo; Fontijne, Daniel; Mann, Stephen (2007). Geometric Algebra for Computer Science. Morgan Kaufmann. ISBN 978-0-12-369465-2. Archived from the original on 2008-09-08. Retrieved 2008-09-12.

harvard.edu (Global: 18^th place; English: 17^th place)

ui.adsabs.harvard.edu

Mamone, Salvatore; Pileio, Giuseppe; Levitt, Malcolm H. (2010). "Orientational Sampling Schemes Based on Four Dimensional Polytopes". Symmetry. 2 (3): 1423–1449. Bibcode:2010Symm....2.1423M. doi:10.3390/sym2031423.
Kunze, Karsten; Schaeben, Helmut (November 2004). "The Bingham distribution of quaternions and its spherical radon transform in texture analysis". Mathematical Geology. 36 (8): 917–943. Bibcode:2004MatGe..36..917K. doi:10.1023/B:MATG.0000048799.56445.59. S2CID 55009081.

hut.fi (Global: low place; English: low place)

lce.hut.fi

Särkkä, Simo (June 28, 2007). "Notes on Quaternions" (PDF). Lce.hut.fi. Archived from the original (PDF) on 5 July 2017.

indiana.edu (Global: 2,113^th place; English: 1,465^th place)

cs.indiana.edu

"Visualizing Quaternions". Morgan-Kaufmann/Elsevier. 2005. Archived from the original on 2007-12-27. Retrieved 2007-01-01.

jstor.org (Global: 26^th place; English: 20^th place)

Clifford, W.K. (1878). "Applications of Grassmann's Extensive Algebra". American Journal of Mathematics. 1 (4). The Johns Hopkins University Press: 350–358. doi:10.2307/2369379. JSTOR 2369379./

loc.gov (Global: 70^th place; English: 63^rd place)

lccn.loc.gov

Altmann, Simon L. (1986). Rotations, Quaternions, and Double Groups. Clarendon Press. Ch. 12. ISBN 0-19-855372-2. LCCN 85013615.

nih.gov (Global: 4^th place; English: 4^th place)

pubmed.ncbi.nlm.nih.gov

Hardy, A.S. (1881). Elements of Quaternions. Vol. 2. Ginn, Heath, & Co. p. 32. doi:10.1126/science.os-2.75.564. ISBN 9781429701860. PMID 17819877. {{cite book}}: ISBN / Date incompatibility (help); |journal= ignored (help)
Hardy, A.S. (1881). Elements of Quaternions. Vol. 2. Ginn, Heath, & Co. p. 65 or 81 (?). doi:10.1126/science.os-2.75.564. ISBN 9781429701860. PMID 17819877. {{cite book}}: |journal= ignored (help)CS1 maint: ignored ISBN errors (link)

nugae.wordpress.com (Global: low place; English: low place)

Conway & Smith 2003, p. 9 Conway, John Horton; Smith, Derek A. (2003). On Quaternions and Octonions: Their Geometry, Arithmetic, and Symmetry. A.K. Peters. ISBN 1-56881-134-9. (review).

projecteuclid.org (Global: 3,707^th place; English: 2,409^th place)

Pujol, J. (2012). "Hamilton, Rodrigues, Gauss, quaternions, and rotations: A historical reassessment". Communications in Mathematical Analysis. 13 (2): 1–14 – via projecteuclid.org.

quantamagazine.org (Global: 6,413^th place; English: 4,268^th place)

Wood, Charlie (6 September 2018). "The strange numbers that birthed modern algebra". Abstractions (blog). Quanta Magazine.

semanticscholar.org (Global: 11^th place; English: 8^th place)

api.semanticscholar.org

Kunze, Karsten; Schaeben, Helmut (November 2004). "The Bingham distribution of quaternions and its spherical radon transform in texture analysis". Mathematical Geology. 36 (8): 917–943. Bibcode:2004MatGe..36..917K. doi:10.1023/B:MATG.0000048799.56445.59. S2CID 55009081.
Park, F.C.; Ravani, Bahram (1997). "Smooth invariant interpolation of rotations". ACM Transactions on Graphics. 16 (3): 277–295. doi:10.1145/256157.256160. S2CID 6192031.

springer.com (Global: 274^th place; English: 309^th place)

link.springer.com

Girard, P. R. (2007). Quaternions, Clifford algebras and relativistic physics. Springer Science & Business Media.

st-andrews.ac.uk (Global: 1,547^th place; English: 1,410^th place)

mathshistory.st-andrews.ac.uk

The Quaternion Association at MacTutor History of Mathematics archive

tcd.ie (Global: 5,099^th place; English: 3,425^th place)

maths.tcd.ie

Hamilton, W.R. (1844–1850). "On quaternions or a new system of imaginaries in algebra". David R. Wilkins collection. Philosophical Magazine. Trinity College Dublin.

tony5m17h.net (Global: low place; English: low place)

Smith, Frank (Tony). "Why not sedenion?". Archived from the original on 14 January 2024. Retrieved 8 June 2018.

ucr.edu (Global: 1,553^rd place; English: 1,008^th place)

math.ucr.edu

Huerta, John (27 September 2010). "Introducing the quaternions" (PDF). Archived (PDF) from the original on 2014-10-21. Retrieved 8 June 2018 – via U.C. Riverside (math.ucr.edu).

web.archive.org (Global: 1^st place; English: 1^st place)

Smith, Frank (Tony). "Why not sedenion?". Archived from the original on 14 January 2024. Retrieved 8 June 2018.
Huerta, John (27 September 2010). "Introducing the quaternions" (PDF). Archived (PDF) from the original on 2014-10-21. Retrieved 8 June 2018 – via U.C. Riverside (math.ucr.edu).
"Visualizing Quaternions". Morgan-Kaufmann/Elsevier. 2005. Archived from the original on 2007-12-27. Retrieved 2007-01-01.
Särkkä, Simo (June 28, 2007). "Notes on Quaternions" (PDF). Lce.hut.fi. Archived from the original (PDF) on 5 July 2017.
"Quaternions and Geometric Algebra". geometricalgebra.net. Archived from the original on 2008-09-08. Retrieved 2008-09-12. See also: Dorst, Leo; Fontijne, Daniel; Mann, Stephen (2007). Geometric Algebra for Computer Science. Morgan Kaufmann. ISBN 978-0-12-369465-2. Archived from the original on 2008-09-08. Retrieved 2008-09-12.

wiley.com (Global: 222^nd place; English: 297^th place)

Gürlebeck, K.; Sprössig, W. (1997). Quaternionic and Clifford calculus for physicists and engineers. New York: John Wiley & Sons.

wolframalpha.com (Global: 4,660^th place; English: 5,295^th place)

"quaternion group". Wolframalpha.com.
"[no title]". Wolframalpha.com. — determinant evaluation via online computer algebra software.

worldcat.org (Global: 5^th place; English: 5^th place)

search.worldcat.org

Perlis, Sam (1971). "Capsule 77: Quaternions". Historical Topics in Algebra. Historical Topics for the Mathematical Classroom. Vol. 31. Reston, VA: National Council of Teachers of Mathematics. p. 39. ISBN 9780873530583. OCLC 195566.
Porteous, Ian R. (1995). "Chapter 8: Quaternions". Clifford Algebras and the Classical Groups (PDF). Cambridge Studies in Advanced Mathematics. Vol. 50. Cambridge: Cambridge University Press. p. 60. doi:10.1017/CBO9780511470912.009. ISBN 9780521551779. MR 1369094. OCLC 32348823.

zbmath.org (Global: 1,923^rd place; English: 1,068^th place)

Hurwitz, A. (1919). Vorlesungen über die Zahlentheorie der Quaternionen. Berlin, DE: J. Springer. JFM 47.0106.01. — concerning Hurwitz quaternions

Quaternion (English Wikipedia)

ams.org (Global: 451st place; English: 277th place)

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cmu.edu (Global: 1,564th place; English: 1,028th place)

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cornell.edu (Global: 332nd place; English: 246th place)

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diva-portal.org (Global: 3,588th place; English: 3,072nd place)

doi.org (Global: 2nd place; English: 2nd place)

ed.ac.uk (Global: 1,871st place; English: 1,234th place)

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harvard.edu (Global: 18th place; English: 17th place)

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indiana.edu (Global: 2,113th place; English: 1,465th place)

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projecteuclid.org (Global: 3,707th place; English: 2,409th place)

quantamagazine.org (Global: 6,413th place; English: 4,268th place)

semanticscholar.org (Global: 11th place; English: 8th place)

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springer.com (Global: 274th place; English: 309th place)

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zbmath.org (Global: 1,923rd place; English: 1,068th place)

ams.org (Global: 451^st place; English: 277^th place)

archive.org (Global: 6^th place; English: 6^th place)

arxiv.org (Global: 69^th place; English: 59^th place)

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cmu.edu (Global: 1,564^th place; English: 1,028^th place)

cornell.edu (Global: 332^nd place; English: 246^th place)

diva-portal.org (Global: 3,588^th place; English: 3,072^nd place)

doi.org (Global: 2^nd place; English: 2^nd place)

ed.ac.uk (Global: 1,871^st place; English: 1,234^th place)

gamedeveloper.com (Global: 4,881^st place; English: 2,796^th place)

harvard.edu (Global: 18^th place; English: 17^th place)

indiana.edu (Global: 2,113^th place; English: 1,465^th place)

jstor.org (Global: 26^th place; English: 20^th place)

loc.gov (Global: 70^th place; English: 63^rd place)

nih.gov (Global: 4^th place; English: 4^th place)

projecteuclid.org (Global: 3,707^th place; English: 2,409^th place)

quantamagazine.org (Global: 6,413^th place; English: 4,268^th place)

semanticscholar.org (Global: 11^th place; English: 8^th place)

springer.com (Global: 274^th place; English: 309^th place)

st-andrews.ac.uk (Global: 1,547^th place; English: 1,410^th place)

tcd.ie (Global: 5,099^th place; English: 3,425^th place)

ucr.edu (Global: 1,553^rd place; English: 1,008^th place)

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wiley.com (Global: 222^nd place; English: 297^th place)

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worldcat.org (Global: 5^th place; English: 5^th place)

zbmath.org (Global: 1,923^rd place; English: 1,068^th place)