Matrix (mathematics) (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Matrix (mathematics)" in English language version.

Last modified: 22:16:34, 10 August 2026 (UTC)

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Gbur (2011), p. 89. Gbur, Greg (2011), Mathematical Methods in Optical Physics and Engineering, Cambridge University Press, Bibcode:2011mmop.book.....G, ISBN 978-0-521-51610-5
Van Loan (2000). Van Loan, Charles F. (2000), "The ubiquitous Kronecker product", Journal of Computational and Applied Mathematics, 123 (1–2): 85–100, Bibcode:2000JCoAM.123...85L, doi:10.1016/S0377-0427(00)00393-9, MR 1798520
Gbur (2011), p. 95. Gbur, Greg (2011), Mathematical Methods in Optical Physics and Engineering, Cambridge University Press, Bibcode:2011mmop.book.....G, ISBN 978-0-521-51610-5
Han, Kim & Noz (1997). Han, D.; Kim, Y. S.; Noz, Marilyn E. (September 1997), "Jones-matrix formalism as a representation of the Lorentz group", Journal of the Optical Society of America A, 14 (9), Optica Publishing Group: 2290, arXiv:physics/9703032, Bibcode:1997JOSAA..14.2290H, doi:10.1364/josaa.14.002290
Gbur (2011), p. 91. Gbur, Greg (2011), Mathematical Methods in Optical Physics and Engineering, Cambridge University Press, Bibcode:2011mmop.book.....G, ISBN 978-0-521-51610-5
Gbur (2011), pp. 99–100. Gbur, Greg (2011), Mathematical Methods in Optical Physics and Engineering, Cambridge University Press, Bibcode:2011mmop.book.....G, ISBN 978-0-521-51610-5
Gbur (2011), pp. 102–103. Gbur, Greg (2011), Mathematical Methods in Optical Physics and Engineering, Cambridge University Press, Bibcode:2011mmop.book.....G, ISBN 978-0-521-51610-5
Gbur (2011), pp. 146–153. Gbur, Greg (2011), Mathematical Methods in Optical Physics and Engineering, Cambridge University Press, Bibcode:2011mmop.book.....G, ISBN 978-0-521-51610-5
Burgess & Moore (2007), section 1.6.3. (SU(3)), section 2.4.3.2. (Kobayashi–Maskawa matrix). Burgess, Cliff; Moore, Guy (2007), The Standard Model. A Primer, Cambridge University Press, Bibcode:2007smp..book.....B, ISBN 978-0-521-86036-9

ams.org (Global: 434^th place; English: 249^th place)

mathscinet.ams.org

Lang (2002), Chapter XIII. 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
Van Loan (2000). Van Loan, Charles F. (2000), "The ubiquitous Kronecker product", Journal of Computational and Applied Mathematics, 123 (1–2): 85–100, Bibcode:2000JCoAM.123...85L, doi:10.1016/S0377-0427(00)00393-9, MR 1798520
Reyes (2025). Reyes, Manuel (2025), "A tour of noncommutative spectral theories", Notices of the American Mathematical Society, 72 (2): 145–153, arXiv:2409.08421, doi:10.1090/noti3100, MR 4854325
Householder (1975), Ch. 7. Householder, Alston S. (1975), The theory of matrices in numerical analysis, New York, NY: Dover Publications, MR 0378371
Tapp (2016). Tapp, Kristopher (2016), Matrix Groups for Undergraduates, Student Mathematical Library, vol. 79 (2nd ed.), Providence, Rhode Island: American Mathematical Society, doi:10.1090/stml/079, ISBN 978-1-4704-2722-1, MR 3468869
Lam (1999), pp. 461–470, Chapter 7, §17 Matrix Rings, §17A Characterization and Examples. Lam, T. Y. (1999), Lectures on Modules and Rings, Graduate Texts in Mathematics, vol. 189, Springer-Verlag, New York, doi:10.1007/978-1-4612-0525-8, ISBN 0-387-98428-3, MR 1653294
Hachenberger & Jungnickel (2020), p. 302, Definition 7.2.1. Hachenberger, Dirk; Jungnickel, Dieter (2020), Topics in Galois Fields, Algorithms and Computation in Mathematics, vol. 29, Cham: Springer, doi:10.1007/978-3-030-60806-4, ISBN 978-3-030-60804-0, MR 4233161
Lang (2002), p. 643, XVII.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), Proposition XIII.4.16. 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
Hungerford (1980), pp. 328–335, VII.1: Matrices and maps. Hungerford, Thomas W. (1980), Algebra, Graduate Texts in Mathematics, vol. 73, Springer-Verlag, New York-Berlin, ISBN 0-387-90518-9, MR 0600654
Cameron (2014). Cameron, Peter J. (2014), "Matrix groups" (PDF), in Hogben, Leslie (ed.), Handbook of Linear Algebra, Discrete Mathematics and its Applications (Boca Raton) (2nd ed.), CRC Press, Boca Raton, FL, ISBN 978-1-4665-0728-9, MR 3013937
See the item "Matrix" in Itô 1987. Itô, Kiyosi, ed. (1987), Encyclopedic Dictionary of Mathematics. Vol. I-IV (2nd ed.), MIT Press, ISBN 978-0-262-09026-1, MR 0901762
"Not much of matrix theory carries over to infinite-dimensional spaces, and what does is not so useful, but it sometimes helps." Halmos 1982, p. 23, Chapter 5. Halmos, Paul Richard (1982), A Hilbert space problem book, Graduate Texts in Mathematics, vol. 19 (2nd ed.), Berlin, DE; New York, NY: Springer-Verlag, ISBN 978-0-387-90685-0, MR 0675952
Brualdi et al. (2018), p. 19. Brualdi, Richard A.; Carmona, Ángeles; van den Driessche, P.; Kirkland, Stephen; Stevanović, Dragan (2018), Encinas, Andrés M.; Mitjana, Margarida (eds.), Combinatorial Matrix Theory, Advanced Courses in Mathematics. CRM Barcelona, Birkhäuser/Springer, Cham, doi:10.1007/978-3-319-70953-6, ISBN 978-3-319-70952-9, MR 3791450
Farid, Khan & Wang (2013), 2087. Farid, F. O.; Khan, Israr Ali; Wang, Qing-Wen (2013), "On matrices over an arbitrary semiring and their generalized inverses", Linear Algebra and its Applications, 439 (7): 2085–2105, doi:10.1016/j.laa.2013.06.002, MR 3090456, Zbl 1283.15016
Reutenauer & Straubing (1984), 351. Reutenauer, Christophe; Straubing, Howard (1984), "Inversion of matrices over a commutative semiring", Journal of Algebra, 88 (2): 350–360, doi:10.1016/0021-8693(84)90070-X, MR 0747520, Zbl 0563.15011
Ghosh (1996), 222. Ghosh, Shamik (1996), "Matrices over semirings", Information Sciences, 90 (1–4): 221–230, doi:10.1016/0020-0255(95)00283-9, MR 1388422, Zbl 0884.15010
Carboni, Kasangian & Walters (1987), 137. Carboni, Aurelio; Kasangian, Stefano; Walters, Robert (1987), "An axiomatics for bicategories of modules", Journal of Pure and Applied Algebra, 45 (2): 127–141, doi:10.1016/0022-4049(87)90065-X, MR 0889588, Zbl 0615.18006
Ward (1997), Ch. 2.8. Ward, J. P. (1997), Quaternions and Cayley numbers, Mathematics and its Applications, vol. 403, Dordrecht, NL: Kluwer Academic Publishers Group, doi:10.1007/978-94-011-5768-1, ISBN 978-0-7923-4513-8, MR 1458894
Krzanowski (1988), p. 60, Ch. 2.2. Krzanowski, Wojtek J. (1988), Principles of multivariate analysis, Oxford Statistical Science Series, vol. 3, The Clarendon Press Oxford University Press, ISBN 978-0-19-852211-9, MR 0969370
Krzanowski (1988), Ch. 4.1. Krzanowski, Wojtek J. (1988), Principles of multivariate analysis, Oxford Statistical Science Series, vol. 3, The Clarendon Press Oxford University Press, ISBN 978-0-19-852211-9, MR 0969370
Knobloch (1994). Knobloch, Eberhard (1994), "From Gauß to Weierstraß: determinant theory and its historical evaluations", in Sasaki, Chikara; Sugiura, Mitsuo; Dauben, Joseph W. (eds.), The Intersection of History and Mathematics, Science Networks: Historical Studies, vol. 15, Birkhäuser, pp. 51–66, doi:10.1007/978-3-0348-7521-9_5, ISBN 3-7643-5029-6, MR 1308079
Hawkins (1975). Hawkins, Thomas (1975), "Cauchy and the spectral theory of matrices", Historia Mathematica, 2: 1–29, doi:10.1016/0315-0860(75)90032-4, MR 0469635
Tarski (1941), p. 40. Tarski, Alfred (1941), Introduction to Logic and the Methodology of Deductive Sciences, Oxford University Press, MR 0003375; reprint of 1946 corrected printing, Dover Publications, 1995, ISBN 0-486-28462-X

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

Brown (1991), p. 1. Brown, William C. (1991), Matrices and vector spaces, New York, NY: Marcel Dekker, ISBN 978-0-8247-8419-5
Brown (1991), Definition I.2.1 (addition), Definition I.2.4 (scalar multiplication), and Definition I.2.33 (transpose). Brown, William C. (1991), Matrices and vector spaces, New York, NY: Marcel Dekker, ISBN 978-0-8247-8419-5
Brown (1991), Theorem I.2.6. Brown, William C. (1991), Matrices and vector spaces, New York, NY: Marcel Dekker, ISBN 978-0-8247-8419-5
Brown (1991), Definition I.2.20. Brown, William C. (1991), Matrices and vector spaces, New York, NY: Marcel Dekker, ISBN 978-0-8247-8419-5
Brown (1991), Theorem I.2.24. Brown, William C. (1991), Matrices and vector spaces, New York, NY: Marcel Dekker, ISBN 978-0-8247-8419-5
Kreyszig (1972), p. 220. Kreyszig, Erwin (1972), Advanced Engineering Mathematics (3rd ed.), New York: Wiley, ISBN 0-471-50728-8.
Kreyszig (1972), pp. 241, 244. Kreyszig, Erwin (1972), Advanced Engineering Mathematics (3rd ed.), New York: Wiley, ISBN 0-471-50728-8.
Brown (1991), I.2.21 and 22. Brown, William C. (1991), Matrices and vector spaces, New York, NY: Marcel Dekker, ISBN 978-0-8247-8419-5
Brown (1991), Definition II.3.3. Brown, William C. (1991), Matrices and vector spaces, New York, NY: Marcel Dekker, ISBN 978-0-8247-8419-5
Brown (1991), Theorem II.3.22. Brown, William C. (1991), Matrices and vector spaces, New York, NY: Marcel Dekker, ISBN 978-0-8247-8419-5
Brown (1991), Definition I.2.28. Brown, William C. (1991), Matrices and vector spaces, New York, NY: Marcel Dekker, ISBN 978-0-8247-8419-5
Brown (1991), Definition I.5.13. Brown, William C. (1991), Matrices and vector spaces, New York, NY: Marcel Dekker, ISBN 978-0-8247-8419-5
Brown (1991), Definition III.2.1. Brown, William C. (1991), Matrices and vector spaces, New York, NY: Marcel Dekker, ISBN 978-0-8247-8419-5
Brown (1991), Theorem III.2.12. Brown, William C. (1991), Matrices and vector spaces, New York, NY: Marcel Dekker, ISBN 978-0-8247-8419-5
Brown (1991), Corollary III.2.16. Brown, William C. (1991), Matrices and vector spaces, New York, NY: Marcel Dekker, ISBN 978-0-8247-8419-5
Brown (1991), Theorem III.3.18. Brown, William C. (1991), Matrices and vector spaces, New York, NY: Marcel Dekker, ISBN 978-0-8247-8419-5
Brown (1991), Definition III.4.1. Brown, William C. (1991), Matrices and vector spaces, New York, NY: Marcel Dekker, ISBN 978-0-8247-8419-5
Brown (1991), Definition III.4.9. Brown, William C. (1991), Matrices and vector spaces, New York, NY: Marcel Dekker, ISBN 978-0-8247-8419-5
Brown (1991), Corollary III.4.10. Brown, William C. (1991), Matrices and vector spaces, New York, NY: Marcel Dekker, ISBN 978-0-8247-8419-5
Baker (2003), Def. 1.30. Baker, Andrew J. (2003), Matrix Groups: An Introduction to Lie Group Theory, Berlin, DE; New York, NY: Springer-Verlag, ISBN 978-1-85233-470-3
Baker (2003), Theorem 1.2. Baker, Andrew J. (2003), Matrix Groups: An Introduction to Lie Group Theory, Berlin, DE; New York, NY: Springer-Verlag, ISBN 978-1-85233-470-3
Ward (1997), Ch. 2.8. Ward, J. P. (1997), Quaternions and Cayley numbers, Mathematics and its Applications, vol. 403, Dordrecht, NL: Kluwer Academic Publishers Group, doi:10.1007/978-94-011-5768-1, ISBN 978-0-7923-4513-8, MR 1458894
Jensen (1999), p. 65–69. Jensen, Frank (1999), Introduction to Computational Chemistry, John Wiley & Sons, ISBN 0-471-98085-4
Lang (1987), Ch. XVI.6. Lang, Serge (1987), Calculus of several variables (3rd ed.), Berlin, DE; New York, NY: Springer-Verlag, ISBN 978-0-387-96405-8
Lang (1987), Ch. XVI.1. Lang, Serge (1987), Calculus of several variables (3rd ed.), Berlin, DE; New York, NY: Springer-Verlag, ISBN 978-0-387-96405-8
Lang 1987, Ch. XVI.5. For a more advanced, and more general statement see Lang 1969, Ch. VI.2. Lang, Serge (1987), Calculus of several variables (3rd ed.), Berlin, DE; New York, NY: Springer-Verlag, ISBN 978-0-387-96405-8 Lang, Serge (1969), Analysis II, Addison-Wesley
Itzykson & Zuber (1980), Ch. 2. Itzykson, Claude; Zuber, Jean-Bernard (1980), Quantum Field Theory, McGraw–Hill, ISBN 0-07-032071-3
Weinberg (1995), Ch. 3. Weinberg, Steven (1995), The Quantum Theory of Fields. Volume I: Foundations, Cambridge University Press, ISBN 0-521-55001-7
Murray, James; Bradley, Henry, eds. (1908), "Matrix", A New English Dictionary on Historical Principles, vol. 6, pt. 2 (M–N), Oxford: Clarendon Press, p. 238
Sylvester (1904), p. 247, Paper 37. Sylvester, J. J. (1904), Baker, H. F. (ed.), The Collected Mathematical Papers of James Joseph Sylvester, Volume I (1837–1853), Cambridge, England: Cambridge University Press
Cayley (1858). Cayley, Arthur (December 1858), "A memoir on the theory of matrices", Philosophical Transactions of the Royal Society of London, 148: 17–37, doi:10.1098/rstl.1858.0002, JSTOR 108649; reprinted in The collected mathematical papers of Arthur Cayley, vol. II, Cambridge University Press, 1889, pp. 475–496.

arxiv.org (Global: 49^th place; English: 31^st place)

Han, Kim & Noz (1997). Han, D.; Kim, Y. S.; Noz, Marilyn E. (September 1997), "Jones-matrix formalism as a representation of the Lorentz group", Journal of the Optical Society of America A, 14 (9), Optica Publishing Group: 2290, arXiv:physics/9703032, Bibcode:1997JOSAA..14.2290H, doi:10.1364/josaa.14.002290
Reyes (2025). Reyes, Manuel (2025), "A tour of noncommutative spectral theories", Notices of the American Mathematical Society, 72 (2): 145–153, arXiv:2409.08421, doi:10.1090/noti3100, MR 4854325
Vassilevska Williams et al. (2024). Vassilevska Williams, Virginia; Xu, Yinzhan; Xu, Zixuan; Zhou, Renfei (2024), "New bounds for matrix multiplication: from alpha to omega", Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 3792–3835, arXiv:2307.07970, doi:10.1137/1.9781611977912.134, ISBN 978-1-61197-791-2
Misra, Bhattacharya & Ghosh (2022). Misra, Chandan; Bhattacharya, Sourangshu; Ghosh, Soumya K. (June 2022), "Stark: Fast and scalable Strassen's matrix multiplication using Apache Spark", IEEE Transactions on Big Data, 8 (3): 699–710, arXiv:1811.07325, doi:10.1109/tbdata.2020.2977326

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

Ramachandra Rao & Bhimasankaram (2000), p. 71. Ramachandra Rao, A.; Bhimasankaram, P. (2000), Linear Algebra, Texts and Readings in Mathematics, vol. 19 (2nd ed.), Springer, ISBN 9789386279019
Hamilton (1987), p. 29. Hamilton, A. G. (1987), A First Course in Linear Algebra: With Concurrent Examples, Cambridge University Press, ISBN 9780521310413
Gentle (1998), pp. 52–53. Gentle, James E. (1998), Numerical Linear Algebra for Applications in Statistics, Springer, ISBN 9780387985428
Bauchau & Craig (2009), p. 915. Bauchau, O. A.; Craig, J. I. (2009), Structural Analysis: With Applications to Aerospace Structures, Solid Mechanics and Its Applications, vol. 163, Springer, ISBN 9789048125166
Johnston (2021), p. 21. Johnston, Nathaniel (2021), Introduction to Linear and Matrix Algebra, Springer Nature, ISBN 9783030528119
For example, for ⁠ $M$ ⁠, see Mello (2017), p. 48; for ⁠ $\operatorname {Mat}$ ⁠, see Axler (1997), p. 50. Mello, David C. (2017), Invitation to Linear Algebra, Textbooks in Mathematics, CRC Press, ISBN 9781498779586 Axler, Sheldon (1997), Linear Algebra Done Right, Undergraduate Texts in Mathematics (2nd ed.), Springer, ISBN 9780387982595
Whitelaw (1991), p. 29. Whitelaw, T. A. (1991), Introduction to Linear Algebra (2nd ed.), CRC Press, p. 29, ISBN 9780751401592
Whitelaw (1991), p. 30. Whitelaw, T. A. (1991), Introduction to Linear Algebra (2nd ed.), CRC Press, p. 29, ISBN 9780751401592
Maxwell (1969), p. 46. Maxwell, E. A. (1969), Algebraic Structure and Matrices, Being Part II of Advanced Algebra, Cambridge University Press
Lancaster & Tismenetsky (1985), pp. 6–7. Lancaster, Peter; Tismenetsky, Miron (1985), The Theory of Matrices: With Applications (2nd ed.), Elsevier, ISBN 9780080519081
Andrilli & Hecker (2022), p. 38, The transpose of a matrix and its properties. Andrilli, Stephen; Hecker, David (2022), Elementary Linear Algebra (6th ed.), Academic Press, ISBN 9780323984263
Lancaster & Tismenetsky (1985), p. 9. Lancaster, Peter; Tismenetsky, Miron (1985), The Theory of Matrices: With Applications (2nd ed.), Elsevier, ISBN 9780080519081
Perrone (2024), p. 119–120. Perrone, Paolo (2024), Starting Category Theory, World Scientific, doi:10.1142/9789811286018_0005, ISBN 978-981-12-8600-1
Lang (1986), p. 71. Lang, Serge (1986), Introduction to Linear Algebra (2nd ed.), Springer, ISBN 9781461210702
Watkins (2002), p. 102. Watkins, David S. (2002), Fundamentals of Matrix Computations, John Wiley & Sons, ISBN 978-0-471-46167-8
Schneider & Barker (2012). Schneider, Hans; Barker, George Phillip (2012), Matrices and Linear Algebra, Dover Books on Mathematics, Courier Dover Corporation, p. 251, ISBN 978-0-486-13930-2
Perlis (1991). Perlis, Sam (1991), Theory of Matrices, Dover books on advanced mathematics, Courier Dover Corporation, p. 103, ISBN 978-0-486-66810-9
Anton (2010). Anton, Howard (2010), Elementary Linear Algebra (10th ed.), John Wiley & Sons, p. 414, ISBN 978-0-470-45821-1
Horn, Roger A.; Johnson, Charles R. (2012), Matrix Analysis (2nd ed.), Cambridge University Press, p. 17, ISBN 978-0-521-83940-2.
Bierens (2004), p. 263. Bierens, Herman J. (2004), Introduction to the Mathematical and Statistical Foundations of Econometrics, Cambridge University Press, ISBN 9780521542241
Johnston (2021), p. 56. Johnston, Nathaniel (2021), Introduction to Linear and Matrix Algebra, Springer Nature, ISBN 9783030528119
Pettofrezzo (1978), p. 60. Pettofrezzo, Anthony J. (1978), Matrices and Transformations, Dover Books on Mathematics, Courier Corporation, ISBN 9780486636344
Jeffrey (2010), p. 264. Jeffrey, Alan (2010), Matrix Operations for Engineers and Scientists: An Essential Guide in Linear Algebra, Springer, ISBN 9789048192748
Anton (2010), p. 27. Anton, Howard (2010), Elementary Linear Algebra (10th ed.), John Wiley & Sons, p. 414, ISBN 978-0-470-45821-1
Anton (2010), p. 68. Anton, Howard (2010), Elementary Linear Algebra (10th ed.), John Wiley & Sons, p. 414, ISBN 978-0-470-45821-1
Anton (2010), p. 62. Anton, Howard (2010), Elementary Linear Algebra (10th ed.), John Wiley & Sons, p. 414, ISBN 978-0-470-45821-1
Anton (2010), Thm. 7.3.2. Anton, Howard (2010), Elementary Linear Algebra (10th ed.), John Wiley & Sons, p. 414, ISBN 978-0-470-45821-1
Mirsky (1990), Theorem 1.4.1. Mirsky, Leonid (1990), An Introduction to Linear Algebra, Courier Dover Publications, ISBN 978-0-486-66434-7
Anton (2010), pp. 317–319. Anton, Howard (2010), Elementary Linear Algebra (10th ed.), John Wiley & Sons, p. 414, ISBN 978-0-470-45821-1
Hachenberger & Jungnickel (2020), p. 302, Definition 7.2.1. Hachenberger, Dirk; Jungnickel, Dieter (2020), Topics in Galois Fields, Algorithms and Computation in Mathematics, vol. 29, Cham: Springer, doi:10.1007/978-3-030-60806-4, ISBN 978-3-030-60804-0, MR 4233161
Riehl (2016), pp. 4-6. Riehl, Emily (2016), Category Theory in Context, Dover, ISBN 9780486809038
Roth (2006), p. 27. Roth, Ron (2006), Introduction to Coding Theory, Cambridge University Press, ISBN 9780521845045
Chahal (2018), pp. 115–116. Chahal, J. S. (2018), Fundamentals of Linear Algebra, CRC Press, ISBN 9780429758119
Meckes & Meckes (2018), pp. 360–361. Meckes, Elizabeth S.; Meckes, Mark W. (2018), Linear Algebra, Cambridge University Press, ISBN 9781316836026
Edwards (2004), p. 80. Edwards, Harold M. (2004), Linear Algebra, Springer Science & Business Media, ISBN 9780817643706
Jeffrey (2010), pp. 54ff, 3.7 Partitioning of matrices. Jeffrey, Alan (2010), Matrix Operations for Engineers and Scientists: An Essential Guide in Linear Algebra, Springer, ISBN 9789048192748
Serre (2007), p. 20. Serre, Denis (2007), Matrices: Theory and Applications, Graduate Texts in Mathematics, vol. 216, Springer Science & Business Media, doi:10.1007/978-1-4419-7683-3, ISBN 9780387227580
Boos (2000), pp. 34–39, 2.2 Dealing with infinite matrices. Boos, Johann (2000), Classical and Modern Methods in Summability, Oxford mathematical monographs, Oxford University Press, ISBN 9780198501657
Grillet (2007), p. 334. Grillet, Pierre Antoine (2007), Abstract Algebra, Graduate Texts in Mathematics, vol. 242 (2nd ed.), Springer, ISBN 9780387715681
Coleman & Van Loan (1988), p. 213. Coleman, Thomas F.; Van Loan, Charles (1988), Handbook for Matrix Computations, Frontiers in Applied Mathematics, vol. 4, SIAM, ISBN 9780898712278
Hazewinkel & Gubareni (2017), p. 151. Hazewinkel, Michiel; Gubareni, Nadiya M. (2017), Algebras, Rings and Modules, Volume 2: Non-commutative Algebras and Rings (2nd ed.), CRC Press
The notation of empty matrix is used differently from some sources like Bernstein (2009), p. 90 use $0_{0\times n}$ , resembling the zero matrix; Hazewinkel & Gubareni (2017), p. 151 use ${\mathfrak {I}}_{0\times n}$ . Bernstein, Dennis S. (2009), Matrix mathematics: theory, facts, and formulas (2nd ed.), Princeton, N.J: Princeton University Press, ISBN 978-1-4008-3334-4 Hazewinkel, Michiel; Gubareni, Nadiya M. (2017), Algebras, Rings and Modules, Volume 2: Non-commutative Algebras and Rings (2nd ed.), CRC Press
West (2020), p. 750. West, Douglas B. (2020), Combinatorial Mathematics, Cambridge University Press, ISBN 9781108889520
Brualdi et al. (2018), p. 19. Brualdi, Richard A.; Carmona, Ángeles; van den Driessche, P.; Kirkland, Stephen; Stevanović, Dragan (2018), Encinas, Andrés M.; Mitjana, Margarida (eds.), Combinatorial Matrix Theory, Advanced Courses in Mathematics. CRM Barcelona, Birkhäuser/Springer, Cham, doi:10.1007/978-3-319-70953-6, ISBN 978-3-319-70952-9, MR 3791450
Abłamowicz (2000), p. 436. Abłamowicz, Rafał (2000), Clifford Algebras and their Applications in Mathematical Physics, Volume 1: Algebra and Physics, Progress in Mathematical Physics, vol. 18, Birkhäuser / Springer, ISBN 9780817641825
McHugh (2025), p. 390, 11.2.3 The expected payoff as a vector–matrix–vector product. McHugh, Andrew (2025), Finite Mathematics: An Introduction with Applications in Business, Social Sciences, and Music, Academic Press, ISBN 9780443290954
Matoušek & Gärtner (2007), pp. 136–137. Matoušek, Jiří; Gärtner, Bernd (2007), Understanding and Using Linear Programming, Springer Science & Business Media, ISBN 9783540307174
Bhaya & Kaszkurewicz (2006), p. 230. Bhaya, Amit; Kaszkurewicz, Eugenius (2006), Control Perspectives on Numerical Algorithms and Matrix Problems, Advances in Design and Control, vol. 10, SIAM, ISBN 9780898716023
Zhang, Yu & Hou (2006), p. 7. Zhang, Yanchun; Yu, Jeffrey Xu; Hou, Jingyu (2006), Web Communities: Analysis and Construction, Springer, ISBN 978-3-540-27737-8
Needham, Joseph; Wang Ling (1959), Science and Civilisation in China, vol. III, Cambridge: Cambridge University Press, p. 117, ISBN 978-0-521-05801-8{{cite book}}: CS1 maint: ignored ISBN errors (link)
The earliest published example is J. J. Sylvester (1850) "Additions to the articles in the September number of this journal, 'On a new class of theorems,' and on Pascal's theorem," The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 37: 363-370. From page 369: "For this purpose, we must commence, not with a square, but with an oblong arrangement of terms consisting, suppose, of m lines and n columns. This does not in itself represent a determinant, but is, as it were, a Matrix out of which we may form various systems of determinants ... "
Sylvester (1904), p. 247, Paper 37. Sylvester, J. J. (1904), Baker, H. F. (ed.), The Collected Mathematical Papers of James Joseph Sylvester, Volume I (1837–1853), Cambridge, England: Cambridge University Press
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Farid, Khan & Wang (2013), 2087. Farid, F. O.; Khan, Israr Ali; Wang, Qing-Wen (2013), "On matrices over an arbitrary semiring and their generalized inverses", Linear Algebra and its Applications, 439 (7): 2085–2105, doi:10.1016/j.laa.2013.06.002, MR 3090456, Zbl 1283.15016
Reutenauer & Straubing (1984), 351. Reutenauer, Christophe; Straubing, Howard (1984), "Inversion of matrices over a commutative semiring", Journal of Algebra, 88 (2): 350–360, doi:10.1016/0021-8693(84)90070-X, MR 0747520, Zbl 0563.15011
Ghosh (1996), 222. Ghosh, Shamik (1996), "Matrices over semirings", Information Sciences, 90 (1–4): 221–230, doi:10.1016/0020-0255(95)00283-9, MR 1388422, Zbl 0884.15010
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