Tensor (English Wikipedia)

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

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alterlab.org

De Lathauwer, Lieven; De Moor, Bart; Vandewalle, Joos (2000). "A Multilinear Singular Value Decomposition" (PDF). SIAM J. Matrix Anal. Appl. 21 (4): 1253–1278. doi:10.1137/S0895479896305696. S2CID 14344372.

archive.org

Schouten, Jan Arnoldus (1954), "Chapter II", Tensor analysis for physicists, Courier Corporation, ISBN 978-0-486-65582-6 {{citation}}: ISBN / Date incompatibility (help)

books.google.com

Kline, Morris (1990). Mathematical Thought From Ancient to Modern Times. Vol. 3. Oxford University Press. ISBN 978-0-19-506137-6.
Sharpe, R.W. (2000). Differential Geometry: Cartan's Generalization of Klein's Erlangen Program. Springer. p. 194. ISBN 978-0-387-94732-7.
Schouten, Jan Arnoldus (1954), "Chapter II", Tensor analysis for physicists, Courier Corporation, ISBN 978-0-486-65582-6 {{citation}}: ISBN / Date incompatibility (help)
Lee, John (2000), Introduction to smooth manifolds, Springer, p. 173, ISBN 978-0-387-95495-0
Bourbaki, N. (1998). "3". Algebra I: Chapters 1-3. Springer. ISBN 978-3-540-64243-5. where the case of finitely generated projective modules is treated. The global sections of sections of a vector bundle over a compact space form a projective module over the ring of smooth functions. All statements for coherent sheaves are true locally.
Reich, Karin (1994). Die Entwicklung des Tensorkalküls. Science networks historical studies. Vol. 11. Birkhäuser. ISBN 978-3-7643-2814-6. OCLC 31468174.
Guo, Hongyu (2021-06-16). What Are Tensors Exactly?. World Scientific. ISBN 978-981-12-4103-1.
Voigt, Woldemar (1898). Die fundamentalen physikalischen Eigenschaften der Krystalle in elementarer Darstellung [The fundamental physical properties of crystals in an elementary presentation]. Von Veit. pp. 20–. Wir wollen uns deshalb nur darauf stützen, dass Zustände der geschilderten Art bei Spannungen und Dehnungen nicht starrer Körper auftreten, und sie deshalb tensorielle, die für sie charakteristischen physikalischen Grössen aber Tensoren nennen. [We therefore want [our presentation] to be based only on [the assumption that] conditions of the type described occur during stresses and strains of non-rigid bodies, and therefore call them "tensorial" but call the characteristic physical quantities for them "tensors".]
Ricci Curbastro, G. (1892). "Résumé de quelques travaux sur les systèmes variables de fonctions associés à une forme différentielle quadratique". Bulletin des Sciences Mathématiques. 2 (16): 167–189.
Pais, Abraham (2005). Subtle Is the Lord: The Science and the Life of Albert Einstein. Oxford University Press. ISBN 978-0-19-280672-7.
Spanier, Edwin H. (2012). Algebraic Topology. Springer. p. 227. ISBN 978-1-4684-9322-1. the Künneth formula expressing the homology of the tensor product...
Hungerford, Thomas W. (2003). Algebra. Springer. p. 168. ISBN 978-0-387-90518-1. ...the classification (up to isomorphism) of modules over an arbitrary ring is quite difficult...
MacLane, Saunders (2013). Categories for the Working Mathematician. Springer. p. 4. ISBN 978-1-4612-9839-7. ...for example the monoid M ... in the category of abelian groups, × is replaced by the usual tensor product...
Wheeler, J.A.; Misner, C.; Thorne, K.S. (1973). Gravitation. W.H. Freeman. p. 83. ISBN 978-0-7167-0344-0.
Maia, M. D. (2011). Geometry of the Fundamental Interactions: On Riemann's Legacy to High Energy Physics and Cosmology. Springer. p. 48. ISBN 978-1-4419-8273-5.
Hogben, Leslie, ed. (2013). Handbook of Linear Algebra (2nd ed.). CRC Press. pp. 15–7. ISBN 978-1-4665-0729-6.
Abraham, Ralph; Marsden, Jerrold E.; Ratiu, Tudor S. (February 1988). "5. Tensors". Manifolds, Tensor Analysis and Applications. Applied Mathematical Sciences. Vol. 75 (2nd ed.). Springer. pp. 338–9. ISBN 978-0-387-96790-5. OCLC 18562688. Elements of T^r_s are called tensors on E, [...].
Lang, Serge (1972). Differential manifolds. Addison-Wesley. ISBN 978-0-201-04166-8.
Schouten, Jan Arnoldus, "§II.8: Densities", Tensor analysis for physicists
McConnell, A.J. (2014) [1957]. Applications of tensor analysis. Dover. p. 28. ISBN 9780486145020.
Kay 1988, p. 27. Kay, David C (1988-04-01). Schaum's Outline of Tensor Calculus. McGraw-Hill. ISBN 978-0-07-033484-7.
Olver, Peter (1995), Equivalence, invariants, and symmetry, Cambridge University Press, p. 77, ISBN 9780521478113
Penrose, Roger (2005). The road to reality: a complete guide to the laws of our universe. Knopf. pp. 203–206.

doi.org

De Lathauwer, Lieven; De Moor, Bart; Vandewalle, Joos (2000). "A Multilinear Singular Value Decomposition" (PDF). SIAM J. Matrix Anal. Appl. 21 (4): 1253–1278. doi:10.1137/S0895479896305696. S2CID 14344372.
Vasilescu, M.A.O.; Terzopoulos, D. (2002). "Multilinear Analysis of Image Ensembles: TensorFaces" (PDF). Computer Vision — ECCV 2002. Lecture Notes in Computer Science. Vol. 2350. pp. 447–460. doi:10.1007/3-540-47969-4_30. ISBN 978-3-540-43745-1. S2CID 12793247. Archived from the original (PDF) on 2022-12-29. Retrieved 2022-12-29.
Kolda, Tamara; Bader, Brett (2009). "Tensor Decompositions and Applications" (PDF). SIAM Review. 51 (3): 455–500. Bibcode:2009SIAMR..51..455K. doi:10.1137/07070111X. S2CID 16074195.
Joyal, André; Street, Ross (1993), "Braided tensor categories", Advances in Mathematics, 102: 20–78, doi:10.1006/aima.1993.1055
Ricci & Levi-Civita 1900. Ricci, Gregorio; Levi-Civita, Tullio (March 1900). "Méthodes de calcul différentiel absolu et leurs applications". Mathematische Annalen. 54 (1–2): 125–201. doi:10.1007/BF01454201. S2CID 120009332.
Goodstein, Judith R. (1982). "The Italian Mathematicians of Relativity". Centaurus. 26 (3): 241–261. Bibcode:1982Cent...26..241G. doi:10.1111/j.1600-0498.1982.tb00665.x.
Segal, I. E. (January 1956). "Tensor Algebras Over Hilbert Spaces. I". Transactions of the American Mathematical Society. 81 (1): 106–134. doi:10.2307/1992855. JSTOR 1992855.
Salviori, Sarah (1972), "On the theory of geometric objects", Journal of Differential Geometry, 7 (1–2): 257–278, doi:10.4310/jdg/1214430830.
Meinrenken, E. (2013). "The spin representation". Clifford Algebras and Lie Theory. Ergebnisse der Mathematik undihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics. Vol. 58. Springer. pp. 49–85. doi:10.1007/978-3-642-36216-3_3. ISBN 978-3-642-36215-6.

emis.de

Hamilton, William Rowan (1854–1855). Wilkins, David R. (ed.). "On some Extensions of Quaternions" (PDF). Philosophical Magazine (7–9): 492–9, 125–137, 261–9, 46–51, 280–290. ISSN 0302-7597. From p. 498: "And if we agree to call the square root (taken with a suitable sign) of this scalar product of two conjugate polynomes, P and KP, the common TENSOR of each, ... "

encyclopediaofmath.org

"Affine tensor", Encyclopedia of Mathematics, EMS Press, 2001 [1994]

harvard.edu

ui.adsabs.harvard.edu

Kolda, Tamara; Bader, Brett (2009). "Tensor Decompositions and Applications" (PDF). SIAM Review. 51 (3): 455–500. Bibcode:2009SIAMR..51..455K. doi:10.1137/07070111X. S2CID 16074195.
Goodstein, Judith R. (1982). "The Italian Mathematicians of Relativity". Centaurus. 26 (3): 241–261. Bibcode:1982Cent...26..241G. doi:10.1111/j.1600-0498.1982.tb00665.x.

jstor.org

Segal, I. E. (January 1956). "Tensor Algebras Over Hilbert Spaces. I". Transactions of the American Mathematical Society. 81 (1): 106–134. doi:10.2307/1992855. JSTOR 1992855.

kolda.net

Kolda, Tamara; Bader, Brett (2009). "Tensor Decompositions and Applications" (PDF). SIAM Review. 51 (3): 455–500. Bibcode:2009SIAMR..51..455K. doi:10.1137/07070111X. S2CID 16074195.

mathunion.org

Nijenhuis, Albert (1960), "Geometric aspects of formal differential operations on tensor fields" (PDF), Proc. Internat. Congress Math.(Edinburgh, 1958), Cambridge University Press, pp. 463–9, archived from the original (PDF) on 2017-10-27, retrieved 2017-10-26.

projecteuclid.org

Salviori, Sarah (1972), "On the theory of geometric objects", Journal of Differential Geometry, 7 (1–2): 257–278, doi:10.4310/jdg/1214430830.

semanticscholar.org

api.semanticscholar.org

De Lathauwer, Lieven; De Moor, Bart; Vandewalle, Joos (2000). "A Multilinear Singular Value Decomposition" (PDF). SIAM J. Matrix Anal. Appl. 21 (4): 1253–1278. doi:10.1137/S0895479896305696. S2CID 14344372.
Vasilescu, M.A.O.; Terzopoulos, D. (2002). "Multilinear Analysis of Image Ensembles: TensorFaces" (PDF). Computer Vision — ECCV 2002. Lecture Notes in Computer Science. Vol. 2350. pp. 447–460. doi:10.1007/3-540-47969-4_30. ISBN 978-3-540-43745-1. S2CID 12793247. Archived from the original (PDF) on 2022-12-29. Retrieved 2022-12-29.
Kolda, Tamara; Bader, Brett (2009). "Tensor Decompositions and Applications" (PDF). SIAM Review. 51 (3): 455–500. Bibcode:2009SIAMR..51..455K. doi:10.1137/07070111X. S2CID 16074195.
Ricci & Levi-Civita 1900. Ricci, Gregorio; Levi-Civita, Tullio (March 1900). "Méthodes de calcul différentiel absolu et leurs applications". Mathematische Annalen. 54 (1–2): 125–201. doi:10.1007/BF01454201. S2CID 120009332.

stackexchange.com

math.stackexchange.com

"Why are Tensors (Vectors of the form a⊗b...⊗z) multilinear maps?". Mathematics Stackexchange. June 5, 2021.

toronto.edu

cs.toronto.edu

Vasilescu, M.A.O.; Terzopoulos, D. (2002). "Multilinear Analysis of Image Ensembles: TensorFaces" (PDF). Computer Vision — ECCV 2002. Lecture Notes in Computer Science. Vol. 2350. pp. 447–460. doi:10.1007/3-540-47969-4_30. ISBN 978-3-540-43745-1. S2CID 12793247. Archived from the original (PDF) on 2022-12-29. Retrieved 2022-12-29.

web.archive.org

Vasilescu, M.A.O.; Terzopoulos, D. (2002). "Multilinear Analysis of Image Ensembles: TensorFaces" (PDF). Computer Vision — ECCV 2002. Lecture Notes in Computer Science. Vol. 2350. pp. 447–460. doi:10.1007/3-540-47969-4_30. ISBN 978-3-540-43745-1. S2CID 12793247. Archived from the original (PDF) on 2022-12-29. Retrieved 2022-12-29.
Nijenhuis, Albert (1960), "Geometric aspects of formal differential operations on tensor fields" (PDF), Proc. Internat. Congress Math.(Edinburgh, 1958), Cambridge University Press, pp. 463–9, archived from the original (PDF) on 2017-10-27, retrieved 2017-10-26.

worldcat.org

search.worldcat.org

Reich, Karin (1994). Die Entwicklung des Tensorkalküls. Science networks historical studies. Vol. 11. Birkhäuser. ISBN 978-3-7643-2814-6. OCLC 31468174.
Hamilton, William Rowan (1854–1855). Wilkins, David R. (ed.). "On some Extensions of Quaternions" (PDF). Philosophical Magazine (7–9): 492–9, 125–137, 261–9, 46–51, 280–290. ISSN 0302-7597. From p. 498: "And if we agree to call the square root (taken with a suitable sign) of this scalar product of two conjugate polynomes, P and KP, the common TENSOR of each, ... "
Abraham, Ralph; Marsden, Jerrold E.; Ratiu, Tudor S. (February 1988). "5. Tensors". Manifolds, Tensor Analysis and Applications. Applied Mathematical Sciences. Vol. 75 (2nd ed.). Springer. pp. 338–9. ISBN 978-0-387-96790-5. OCLC 18562688. Elements of T^r_s are called tensors on E, [...].

zenodo.org

Ricci & Levi-Civita 1900. Ricci, Gregorio; Levi-Civita, Tullio (March 1900). "Méthodes de calcul différentiel absolu et leurs applications". Mathematische Annalen. 54 (1–2): 125–201. doi:10.1007/BF01454201. S2CID 120009332.