Vector space (English Wikipedia)

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

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Lang 2002. Lang, Serge (2002), Algebra, Graduate Texts in Mathematics, vol. 211 (Revised third ed.), New York: Springer-Verlag, ISBN 978-0-387-95385-4, MR 1878556
Blass 1984. Blass, Andreas (1984), "Existence of bases implies the axiom of choice" (PDF), Axiomatic set theory, Contemporary Mathematics volume 31, Providence, R.I.: American Mathematical Society, pp. 31–33, ISBN 978-0-8218-5026-8, MR 0763890
Dorier 1995. Dorier, Jean-Luc (1995), "A general outline of the genesis of vector space theory", Historia Mathematica, 22 (3): 227–261, doi:10.1006/hmat.1995.1024, MR 1347828
Dorier 1995; Moore 1995. Dorier, Jean-Luc (1995), "A general outline of the genesis of vector space theory", Historia Mathematica, 22 (3): 227–261, doi:10.1006/hmat.1995.1024, MR 1347828 Moore, Gregory H. (1995), "The axiomatization of linear algebra: 1875–1940", Historia Mathematica, 22 (3): 262–303, doi:10.1006/hmat.1995.1025
Lang 2002, ch. V.1. Lang, Serge (2002), Algebra, Graduate Texts in Mathematics, vol. 211 (Revised third ed.), New York: Springer-Verlag, ISBN 978-0-387-95385-4, MR 1878556
Lang 2002, ch. XVI.1. Lang, Serge (2002), Algebra, Graduate Texts in Mathematics, vol. 211 (Revised third ed.), New York: Springer-Verlag, ISBN 978-0-387-95385-4, MR 1878556
Naber 2003, ch. 1.2. Naber, Gregory L. (2003), The geometry of Minkowski spacetime, New York: Dover Publications, ISBN 978-0-486-43235-9, MR 2044239
Kreyszig 1989, §4.11-5 Kreyszig, Erwin (1989), Introductory functional analysis with applications, Wiley Classics Library, New York: John Wiley & Sons, ISBN 978-0-471-50459-7, MR 0992618
Kreyszig 1989, §1.5-5 Kreyszig, Erwin (1989), Introductory functional analysis with applications, Wiley Classics Library, New York: John Wiley & Sons, ISBN 978-0-471-50459-7, MR 0992618
Lang 2002, ch. III.1, p. 121. Lang, Serge (2002), Algebra, Graduate Texts in Mathematics, vol. 211 (Revised third ed.), New York: Springer-Verlag, ISBN 978-0-387-95385-4, MR 1878556
Eisenbud 1995, ch. 1.6. Eisenbud, David (1995), Commutative algebra, Graduate Texts in Mathematics, vol. 150, Berlin, New York: Springer-Verlag, ISBN 978-0-387-94269-8, MR 1322960
Lang 2002, ch. XVI.7. Lang, Serge (2002), Algebra, Graduate Texts in Mathematics, vol. 211 (Revised third ed.), New York: Springer-Verlag, ISBN 978-0-387-95385-4, MR 1878556
Lang 2002, ch. XVI.8. Lang, Serge (2002), Algebra, Graduate Texts in Mathematics, vol. 211 (Revised third ed.), New York: Springer-Verlag, ISBN 978-0-387-95385-4, MR 1878556
Atiyah 1989. Atiyah, Michael Francis (1989), K-theory, Advanced Book Classics (2nd ed.), Addison-Wesley, ISBN 978-0-201-09394-0, MR 1043170

archive.org

Brown 1991, p. 86. Brown, William A. (1991), Matrices and vector spaces, New York: M. Dekker, ISBN 978-0-8247-8419-5
Brown 1991, p. 87. Brown, William A. (1991), Matrices and vector spaces, New York: M. Dekker, ISBN 978-0-8247-8419-5
Springer 2000, p. 185; Brown 1991, p. 86. Springer, T.A. (2000), Linear Algebraic Groups, Springer, ISBN 978-0-8176-4840-4 Brown, William A. (1991), Matrices and vector spaces, New York: M. Dekker, ISBN 978-0-8247-8419-5
Brown 1991, p. 94. Brown, William A. (1991), Matrices and vector spaces, New York: M. Dekker, ISBN 978-0-8247-8419-5
Brown 1991, pp. 99–101. Brown, William A. (1991), Matrices and vector spaces, New York: M. Dekker, ISBN 978-0-8247-8419-5
Brown 1991, p. 92. Brown, William A. (1991), Matrices and vector spaces, New York: M. Dekker, ISBN 978-0-8247-8419-5
Kreyszig 1999, Chapter 11. Kreyszig, Erwin (1999), Advanced Engineering Mathematics (8th ed.), New York: John Wiley & Sons, ISBN 978-0-471-15496-9

books.google.com

Springer 2000, p. 185; Brown 1991, p. 86. Springer, T.A. (2000), Linear Algebraic Groups, Springer, ISBN 978-0-8176-4840-4 Brown, William A. (1991), Matrices and vector spaces, New York: M. Dekker, ISBN 978-0-8247-8419-5
Stoll & Wong 1968, p. 14. Stoll, R. R.; Wong, E. T. (1968), Linear Algebra, Academic Press
Lang 1987, p. 10–11; Anton & Rorres 2010, p. 212. Lang, Serge (1987), Linear algebra, Undergraduate Texts in Mathematics (3rd ed.), Springer, doi:10.1007/978-1-4757-1949-9, ISBN 978-1-4757-1949-9
Joshi 1989, p. 450. Joshi, K. D. (1989), Foundations of Discrete Mathematics, John Wiley & Sons
Heil 2011, p. 126. Heil, Christopher (2011), A Basis Theory Primer: Expanded Edition, Applied and Numerical Harmonic Analysis, Birkhäuser, doi:10.1007/978-0-8176-4687-5, ISBN 978-0-8176-4687-5
Halmos 1948, p. 12. Halmos, Paul R. (1948), Finite Dimensional Vector Spaces, vol. 7, Princeton University Press
Guo 2021. Guo, Hongyu (2021-06-16), What Are Tensors Exactly?, World Scientific, ISBN 978-981-12-4103-1
Kreyszig 2020, p. 355. Kreyszig, Erwin (2020), Advanced Engineering Mathematics, John Wiley & Sons, ISBN 978-1-119-45592-9
Kreyszig 2020, p. 358–359. Kreyszig, Erwin (2020), Advanced Engineering Mathematics, John Wiley & Sons, ISBN 978-1-119-45592-9
Jain 2001, p. 11. Jain, M. C. (2001), Vector Spaces and Matrices in Physics, CRC Press, ISBN 978-0-8493-0978-6

cornell.edu

historical.library.cornell.edu

Hamilton 1853. Hamilton, William Rowan (1853), Lectures on Quaternions, Royal Irish Academy

dml.cz

Bolzano 1804. Bolzano, Bernard (1804), Betrachtungen über einige Gegenstände der Elementargeometrie (Considerations of some aspects of elementary geometry) (in German)

doi.org

Lang 1987, p. 10–11; Anton & Rorres 2010, p. 212. Lang, Serge (1987), Linear algebra, Undergraduate Texts in Mathematics (3rd ed.), Springer, doi:10.1007/978-1-4757-1949-9, ISBN 978-1-4757-1949-9
Heil 2011, p. 126. Heil, Christopher (2011), A Basis Theory Primer: Expanded Edition, Applied and Numerical Harmonic Analysis, Birkhäuser, doi:10.1007/978-0-8176-4687-5, ISBN 978-0-8176-4687-5
Dorier 1995. Dorier, Jean-Luc (1995), "A general outline of the genesis of vector space theory", Historia Mathematica, 22 (3): 227–261, doi:10.1006/hmat.1995.1024, MR 1347828
Moore 1995, pp. 268–271. Moore, Gregory H. (1995), "The axiomatization of linear algebra: 1875–1940", Historia Mathematica, 22 (3): 262–303, doi:10.1006/hmat.1995.1025
Banach 1922. Banach, Stefan (1922), "Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales (On operations in abstract sets and their application to integral equations)" (PDF), Fundamenta Mathematicae (in French), 3: 133–181, doi:10.4064/fm-3-1-133-181, ISSN 0016-2736
Dorier 1995; Moore 1995. Dorier, Jean-Luc (1995), "A general outline of the genesis of vector space theory", Historia Mathematica, 22 (3): 227–261, doi:10.1006/hmat.1995.1024, MR 1347828 Moore, Gregory H. (1995), "The axiomatization of linear algebra: 1875–1940", Historia Mathematica, 22 (3): 262–303, doi:10.1006/hmat.1995.1025
Lang 1987, ch. I.1. Lang, Serge (1987), Linear algebra, Undergraduate Texts in Mathematics (3rd ed.), Springer, doi:10.1007/978-1-4757-1949-9, ISBN 978-1-4757-1949-9
Lang 1987, ch. VI.3.. Lang, Serge (1987), Linear algebra, Undergraduate Texts in Mathematics (3rd ed.), Springer, doi:10.1007/978-1-4757-1949-9, ISBN 978-1-4757-1949-9
Lang 1987, ch. IV.4, Corollary, p. 106. Lang, Serge (1987), Linear algebra, Undergraduate Texts in Mathematics (3rd ed.), Springer, doi:10.1007/978-1-4757-1949-9, ISBN 978-1-4757-1949-9
Lang 1987, Example IV.2.6. Lang, Serge (1987), Linear algebra, Undergraduate Texts in Mathematics (3rd ed.), Springer, doi:10.1007/978-1-4757-1949-9, ISBN 978-1-4757-1949-9
Lang 1987, ch. VI.6. Lang, Serge (1987), Linear algebra, Undergraduate Texts in Mathematics (3rd ed.), Springer, doi:10.1007/978-1-4757-1949-9, ISBN 978-1-4757-1949-9
Lang 1987, Theorem IV.2.1, p. 95. Lang, Serge (1987), Linear algebra, Undergraduate Texts in Mathematics (3rd ed.), Springer, doi:10.1007/978-1-4757-1949-9, ISBN 978-1-4757-1949-9
Lang 1987, ch. V.1. Lang, Serge (1987), Linear algebra, Undergraduate Texts in Mathematics (3rd ed.), Springer, doi:10.1007/978-1-4757-1949-9, ISBN 978-1-4757-1949-9
Lang 1987, ch. V.3., Corollary, p. 106. Lang, Serge (1987), Linear algebra, Undergraduate Texts in Mathematics (3rd ed.), Springer, doi:10.1007/978-1-4757-1949-9, ISBN 978-1-4757-1949-9
Lang 1987, Theorem VII.9.8, p. 198. Lang, Serge (1987), Linear algebra, Undergraduate Texts in Mathematics (3rd ed.), Springer, doi:10.1007/978-1-4757-1949-9, ISBN 978-1-4757-1949-9
& Lang 1987, ch. IX.4. Lang, Serge (1987), Linear algebra, Undergraduate Texts in Mathematics (3rd ed.), Springer, doi:10.1007/978-1-4757-1949-9, ISBN 978-1-4757-1949-9
Lang 1987, ch. IV.3.. Lang, Serge (1987), Linear algebra, Undergraduate Texts in Mathematics (3rd ed.), Springer, doi:10.1007/978-1-4757-1949-9, ISBN 978-1-4757-1949-9
Eisenberg & Guy 1979. Eisenberg, Murray; Guy, Robert (1979), "A proof of the hairy ball theorem", The American Mathematical Monthly, 86 (7): 572–574, doi:10.2307/2320587, JSTOR 2320587
Grillet 2007. Grillet, Pierre Antoine (2007), Abstract algebra, vol. 242, Springer Science & Business Media, doi:10.1007/978-0-387-71568-1, ISBN 978-0-387-71568-1

emath.fr

mathdoc.emath.fr

Möbius 1827. Möbius, August Ferdinand (1827), Der Barycentrische Calcul : ein neues Hülfsmittel zur analytischen Behandlung der Geometrie (Barycentric calculus: a new utility for an analytic treatment of geometry) (in German), archived from the original on 2006-11-23

icm.edu.pl

matwbn.icm.edu.pl

Banach 1922. Banach, Stefan (1922), "Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales (On operations in abstract sets and their application to integral equations)" (PDF), Fundamenta Mathematicae (in French), 3: 133–181, doi:10.4064/fm-3-1-133-181, ISSN 0016-2736

jstor.org

Eisenberg & Guy 1979. Eisenberg, Murray; Guy, Robert (1979), "A proof of the hairy ball theorem", The American Mathematical Monthly, 86 (7): 572–574, doi:10.2307/2320587, JSTOR 2320587

lyryx.com

Nicholson 2018, ch. 7.3. Nicholson, W. Keith (2018), Linear Algebra with Applications, Lyryx
Nicholson 2018, ch. 10.4. Nicholson, W. Keith (2018), Linear Algebra with Applications, Lyryx
Nicholson 2018, ch. 7.4. Nicholson, W. Keith (2018), Linear Algebra with Applications, Lyryx

matrixanalysis.com

Meyer 2000, Example 5.13.5, p. 436. Meyer, Carl D. (2000), Matrix Analysis and Applied Linear Algebra, SIAM, ISBN 978-0-89871-454-8
Meyer 2000, Exercise 5.13.15–17, p. 442. Meyer, Carl D. (2000), Matrix Analysis and Applied Linear Algebra, SIAM, ISBN 978-0-89871-454-8

umich.edu

math.lsa.umich.edu

Blass 1984. Blass, Andreas (1984), "Existence of bases implies the axiom of choice" (PDF), Axiomatic set theory, Contemporary Mathematics volume 31, Providence, R.I.: American Mathematical Society, pp. 31–33, ISBN 978-0-8218-5026-8, MR 0763890

unige.ch

archive-ouverte.unige.ch

Dorier 1995. Dorier, Jean-Luc (1995), "A general outline of the genesis of vector space theory", Historia Mathematica, 22 (3): 227–261, doi:10.1006/hmat.1995.1024, MR 1347828
Dorier 1995; Moore 1995. Dorier, Jean-Luc (1995), "A general outline of the genesis of vector space theory", Historia Mathematica, 22 (3): 227–261, doi:10.1006/hmat.1995.1024, MR 1347828 Moore, Gregory H. (1995), "The axiomatization of linear algebra: 1875–1940", Historia Mathematica, 22 (3): 262–303, doi:10.1006/hmat.1995.1025

web.archive.org

Möbius 1827. Möbius, August Ferdinand (1827), Der Barycentrische Calcul : ein neues Hülfsmittel zur analytischen Behandlung der Geometrie (Barycentric calculus: a new utility for an analytic treatment of geometry) (in German), archived from the original on 2006-11-23

worldcat.org

Banach 1922. Banach, Stefan (1922), "Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales (On operations in abstract sets and their application to integral equations)" (PDF), Fundamenta Mathematicae (in French), 3: 133–181, doi:10.4064/fm-3-1-133-181, ISSN 0016-2736
Schaefer & Wolff 1999, pp. 204–205. Schaefer, Helmut H.; Wolff, Manfred P. (1999). Topological Vector Spaces. GTM. Vol. 8 (Second ed.). New York, NY: Springer New York Imprint Springer. ISBN 978-1-4612-7155-0. OCLC 840278135.
Schaefer & Wolff 1999, p. 7. Schaefer, Helmut H.; Wolff, Manfred P. (1999). Topological Vector Spaces. GTM. Vol. 8 (Second ed.). New York, NY: Springer New York Imprint Springer. ISBN 978-1-4612-7155-0. OCLC 840278135.