Editing Exterior algebra (section)

=== Other references and further reading ===
<!--For works inessential to the article, though these may also have been referenced in passing.-->
{{refbegin|30em}}
* {{citation |last=Browne |first=J.M. |year=2007 |title=Grassmann algebra – Exploring applications of Extended Vector Algebra with Mathematica |url=http://www.grassmannalgebra.info/grassmannalgebra/book/index.htm |access-date=2007-05-09 |archive-date=2009-02-19 |archive-url=https://web.archive.org/web/20090219180241/http://grassmannalgebra.info/grassmannalgebra/book/index.htm |url-status=usurped }}
*: An introduction to the exterior algebra, and [[geometric algebra]], with a focus on applications.  Also includes a history section and bibliography.
* {{citation |last=Spivak |first=Michael |author-link=Michael Spivak |year=1965 |title=Calculus on manifolds |publisher=Addison-Wesley |isbn=978-0-8053-9021-6}}
*: Includes applications of the exterior algebra to differential forms, specifically focused on [[integral|integration]] and [[Stokes's theorem]].  The notation <math display=inline>{\textstyle\bigwedge}^{\!k} V </math> in this text is used to mean the space of alternating ''k''-forms on ''V''; i.e., for Spivak <math display=inline>{\textstyle\bigwedge}^{\!k} V </math> is what this article would call <math display=inline>{\textstyle\bigwedge}^{\!k} V^*. </math>  Spivak discusses this in Addendum 4.
* {{citation |last=Strang |first=G. |author-link=Gilbert Strang |year=1993 |title=Introduction to linear algebra |publisher=Wellesley-Cambridge Press |isbn=978-0-9614088-5-5}}
*: Includes an elementary treatment of the axiomatization of determinants as signed areas, volumes, and higher-dimensional volumes.
* {{springer |id=E/e037080 |title=Exterior algebra |author=Onishchik, A.L. }}
* {{citation |first=Fleming |last=Wendell |chapter=7. Exterior algebra and differential calculus |chapter-url={{GBurl|v-QlBQAAQBAJ|p=275}} |title=Functions of Several Variables |publisher=Springer |edition=2nd |orig-year=1977 |date=2012 |isbn=978-1-4684-9461-7 |pages=275–320 |url= }}
*: This textbook in [[multivariate calculus]] introduces the exterior algebra of differential forms adroitly into the calculus sequence for colleges.
* {{cite book | last1 = Shafarevich | first1 = I.R. | author-link1 = Igor Shafarevich | last2 = Remizov | first2 = A.O. | year = 2012 | title = Linear Algebra and Geometry | publisher = [[Springer Science+Business Media|Springer]] | isbn = 978-3-642-30993-9 | url = https://www.springer.com/mathematics/algebra/book/978-3-642-30993-9 }}
*: Chapter 10: The Exterior Product and Exterior Algebras
* [http://neo-classical-physics.info/uploads/3/0/6/5/3065888/burali-forti_-_grassman_and_proj._geom..pdf "The Grassmann method in projective geometry"] A compilation of English translations of three notes by Cesare Burali-Forti on the application of exterior algebra to projective geometry
* [http://neo-classical-physics.info/uploads/3/0/6/5/3065888/burali-forti_-_diff._geom._following_grassmann.pdf C. Burali-Forti, "Introduction to Differential Geometry, following the method of H. Grassmann"] An English translation of an early book on the geometric applications of exterior algebras
* [http://neo-classical-physics.info/uploads/3/0/6/5/3065888/grassmann_-_mechanics_and_extensions.pdf "Mechanics, according to the principles of the theory of extension"] An English translation of one Grassmann's papers on the applications of exterior algebra
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{{Linear algebra}}
{{tensors}}

[[Category:Algebras]]
[[Category:Multilinear algebra]]
[[Category:Differential forms]]