Editing Determinant (section)

== References ==
{{See also|Linear algebra#Further reading}}
* {{Citation
 | last = Anton
 | first = Howard
 | year = 2005
 | title = Elementary Linear Algebra (Applications Version)
 | publisher = Wiley International
 | edition = 9th
}}
* {{Cite book|last=Axler|first=Sheldon Jay|title=Linear Algebra Done Right|publisher=[[Springer Science+Business Media|Springer]]|year=2015|isbn=978-3-319-11079-0|edition=3rd|author-link=Sheldon Axler}}
* {{citation|first=Erwin|last=Bareiss|title= Sylvester's Identity and Multistep Integer-Preserving Gaussian Elimination|pages=565–578|url=https://www.ams.org/journals/mcom/1968-22-103/S0025-5718-1968-0226829-0/S0025-5718-1968-0226829-0.pdf |archive-url=https://web.archive.org/web/20121025053848/http://www.ams.org/journals/mcom/1968-22-103/S0025-5718-1968-0226829-0/S0025-5718-1968-0226829-0.pdf |archive-date=2012-10-25 |url-status=live|journal=Mathematics of Computation|year=1968|volume=22|issue=102|doi=10.2307/2004533|jstor=2004533}}
* {{Citation | last1=de Boor | first1=Carl | author1-link=Carl R. de Boor | title=An empty exercise | url=http://ftp.cs.wisc.edu/Approx/empty.pdf |archive-url=https://web.archive.org/web/20060901214854/http://ftp.cs.wisc.edu/Approx/empty.pdf |archive-date=2006-09-01 |url-status=live | doi=10.1145/122272.122273 |year=1990 | journal=ACM SIGNUM Newsletter | volume=25 | issue=2 | pages=3–7| s2cid=62780452 }}
* {{Citation|last1=Bourbaki|first1=Nicolas|title=Algebra I, Chapters 1-3|isbn= 9783540642435|publisher=Springer|year=1998}}
* {{cite journal |first1=J. R. |last1=Bunch |first2=J. E. |last2=Hopcroft |title=Triangular Factorization and Inversion by Fast Matrix Multiplication |journal=[[Mathematics of Computation]] |volume=28 |year=1974 |issue= 125|pages=231–236 |doi=10.1090/S0025-5718-1974-0331751-8 |doi-access=free |hdl=1813/6003 |hdl-access=free }}
* {{Citation|title=Abstract algebra|last1=Dummit|first1=David S.|last2=Foote|first2=Richard M.|date=2004|publisher=Wiley|isbn=9780471452348|edition=3rd|location=Hoboken, NJ|oclc=248917264}}
* {{Citation|last1=Fisikopoulos|journal=[[Computational Geometry (journal)|Computational Geometry]]|volume=54|year=2016|pages=1–16|title=Faster geometric algorithms via dynamic determinant computation|first1=Vissarion|first2=Luis|last2=Peñaranda|doi=10.1016/j.comgeo.2015.12.001|doi-access=free|arxiv=1206.7067}}
* {{Citation|last1=Garibaldi|first1=Skip|title=The characteristic polynomial and determinant are not ad hoc constructions|journal=American Mathematical Monthly|volume=111|year=2004|issue=9|pages=761–778|mr=2104048|doi=10.2307/4145188|jstor=4145188|arxiv=math/0203276}}
* {{Cite journal|doi=10.1016/j.jda.2011.06.007|title=A condensation-based application of Cramer's rule for solving large-scale linear systems|journal=Journal of Discrete Algorithms|volume=10|pages=98–109|year=2012|last1=Habgood|first1=Ken|last2=Arel|first2=Itamar|url=https://hal.archives-ouvertes.fr/hal-01500199/file/HA.pdf |archive-url=https://web.archive.org/web/20190505060158/https://hal.archives-ouvertes.fr/hal-01500199/file/HA.pdf |archive-date=2019-05-05 |url-status=live|doi-access=free}}
* {{Citation|last=Harris|first=Frank E.|year=2014|title=Mathematics for Physical Science and Engineering|publisher=Elsevier|isbn=9780128010495}}
* {{Citation|last=Kleiner|first=Israel|editor1-first=Israel|editor1-last=Kleiner|title=A history of abstract algebra|year=2007|publisher=Birkhäuser|isbn=978-0-8176-4684-4|mr=2347309|doi=10.1007/978-0-8176-4685-1}}
* {{Citation|first1=Joseph P.S.|last1=Kung|first2=Gian-Carlo|last2=Rota|first3=Catherine|last3=Yan|author3-link=Catherine H. Yan|title=[[Combinatorics: The Rota Way]]|publisher=Cambridge University Press|year=2009|isbn=9780521883894}}
* {{Citation
 | last = Lay
 | first = David C.
 | date = August 22, 2005
 | title = Linear Algebra and Its Applications
 | publisher = Addison Wesley
 | edition = 3rd
 | isbn = 978-0-321-28713-7
}}
* {{Citation|last1=Lombardi|first1=Henri|last2=Quitté|first2=Claude|title=Commutative Algebra: Constructive Methods|year=2015|isbn=9789401799447|publisher=Springer}}
* {{Citation|last=Mac Lane|first=Saunders|title=Categories for the Working Mathematician|year=1998|series=Graduate Texts in Mathematics '''5'''|edition=2nd|publisher=Springer-Verlag|isbn=0-387-98403-8|author-link=Saunders Mac Lane|title-link=Categories for the Working Mathematician}}
* {{Citation |last = Meyer |first = Carl D. |date = February 15, 2001 |title = Matrix Analysis and Applied Linear Algebra |publisher = Society for Industrial and Applied Mathematics (SIAM) |isbn = 978-0-89871-454-8 |url = http://www.matrixanalysis.com/DownloadChapters.html |url-status = dead |archive-url = https://web.archive.org/web/20091031193126/http://matrixanalysis.com/DownloadChapters.html |archive-date = 2009-10-31
}}
* {{citation | last=Muir | first=Thomas | author-link=Thomas Muir (mathematician) | title=A treatise on the theory of determinants | others=Revised and enlarged by William H. Metzler | orig-year=1933 | year=1960 | publisher=Dover | location=New York, NY }}
* {{Citation
 | last = Poole
 | first = David
 | year = 2006
 | title = Linear Algebra: A Modern Introduction
 | publisher = Brooks/Cole
 | edition = 2nd
 | isbn = 0-534-99845-3
}}
* [[G. Baley Price]] (1947) "Some identities in the theory of determinants", [[American Mathematical Monthly]] 54:75–90 {{mr|id=0019078}}
*{{Cite book|last1=Horn|first1=Roger Alan|title=Matrix Analysis|last2=Johnson|first2=Charles Royal|publisher=[[Cambridge University Press]]|year=2018|isbn=978-0-521-54823-6|edition=2nd|author-link=Roger Horn|author-link2=Charles Royal Johnson|orig-year=1985}}
* {{Citation|last=Lang|first=Serge|title=Introduction to Linear Algebra|edition=2|year=1985|publisher=Springer|isbn=9780387962054|series=Undergraduate Texts in Mathematics}}
* {{Citation|last=Lang|first=Serge|title=Linear Algebra|edition=3|year=1987|publisher=Springer|isbn=9780387964126|series=Undergraduate Texts in Mathematics}}
* {{cite book|last1=Lang|first1=Serge|title=Algebra|date=2002|publisher=Springer|location=New York, NY|isbn=978-0-387-95385-4|series=Graduate Texts in Mathematics}}
* {{Citation
 | last = Leon
 | first = Steven J.
 | year = 2006
 | title = Linear Algebra With Applications
 | publisher = Pearson Prentice Hall
 | edition = 7th
}}
*{{Citation|last1=Rote|first1=Günter|chapter=Division-free algorithms for the determinant and the Pfaffian: algebraic and combinatorial approaches|title=Computational discrete mathematics|series=Lecture Notes in Comput. Sci.|volume=2122|pages=119–135|publisher=Springer|year=2001|mr=1911585|doi=10.1007/3-540-45506-X_9|isbn=978-3-540-42775-9|doi-access=free|chapter-url=https://page.inf.fu-berlin.de/~rote/Papers/pdf/Division-free+algorithms.pdf|access-date=2020-06-04|archive-date=2007-02-01|archive-url=https://web.archive.org/web/20070201145100/http://page.inf.fu-berlin.de/~rote/Papers/pdf/Division-free+algorithms.pdf|url-status=dead}}
* {{Citation | last1 = Trefethen | first1 = Lloyd | last2 = Bau III | first2 = David | location=Philadelphia | isbn=978-0-89871-361-9 | year = 1997 | title = Numerical Linear Algebra | publisher = SIAM | edition = 1st}}

=== Historical references ===
* {{Citation|last=Bourbaki|first=Nicolas|title=Elements of the history of mathematics|translator-first=John|translator-last=Meldrum|translator-link=John D. P. Meldrum|publisher=Springer|year=1994|isbn=3-540-19376-6|doi=10.1007/978-3-642-61693-8}}
* {{Citation|last=Cajori|first=Florian|title=A history of mathematical notations: Including Vol. I. Notations in elementary mathematics; Vol. II. Notations mainly in higher mathematics, Reprint of the 1928 and 1929 originals|publisher=Dover|year=1993|isbn=0-486-67766-4|mr=3363427}}
* {{Citation|last=Bézout|first=Étienne|year=1779|location=Paris|title=Théorie générale des equations algébriques|url=https://gallica.bnf.fr/ark:/12148/bpt6k106053p.image}}
* {{Citation|last=Cayley|first=Arthur|title=On a theorem in the geometry of position|journal=Cambridge Mathematical Journal|volume=2|pages=267–271|year=1841}}
* {{Citation|last=Cramer|first=Gabriel|title=Introduction à l'analyse des lignes courbes algébriques|year=1750|doi=10.3931/e-rara-4048|location=Genève|publisher=Frères Cramer & Cl. Philibert}}
* {{Citation|last=Eves|first=Howard|title=An introduction to the history of mathematics|edition=6|publisher=Saunders College Publishing|year=1990|isbn=0-03-029558-0|mr=1104435}}
* {{Citation|editor1-last=Grattan-Guinness|editor1-first=I.|title=Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences|volume=1|year=2003|isbn=9780801873966|publisher=[[Johns Hopkins University Press]]}}
* {{Citation|last1=Jacobi|first1=Carl Gustav Jakob|author1-link=Carl Gustav Jakob Jacobi|title=De Determinantibus functionalibus|url=https://www.digizeitschriften.de/dms/img/?PID=GDZPPN002142724&physid=phys325#navi|journal=Journal für die reine und angewandte Mathematik|year=1841|volume=1841|issue=22|pages=320–359|doi=10.1515/crll.1841.22.319|s2cid=123637858}}
* {{Citation|last=Laplace|first=Pierre-Simon, de|author-link=Pierre-Simon Laplace|title=Recherches sur le calcul intégral et sur le systéme du monde|journal=Histoire de l'Académie Royale des Sciences|location=Paris|year=1772|issue=seconde partie|pages=267–376|url=https://gallica.bnf.fr/ark:/12148/bpt6k77596b/f374}}
* [http://www.totoha.net/archiv/scott1880.pdf Robert Forsyth Scott (1880): ''A Treatise on the Theory of Determinants and Their Applications in Analysis and Geometry'', Cambridge University Press]
* [https://www.jstor.org/stable/1967268 E. R. Hedrick: ''On Three Dimensional Determinants'', Annals of Mathematics, Vol.1, No.1/4 (1899-1900), pp.49-67 (19pages). https://doi.org/10.2307/1967268] # Note: This is not the ordinal determinant.