Matrix (mathematics) (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Matrix (mathematics)" 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
Householder 1975, Ch. 7 Householder, Alston S. (1975), The theory of matrices in numerical analysis, New York, NY: Dover Publications, MR 0378371
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
Lang 2002, XVII.1, p. 643 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
"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
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, Ch. 2.2., p. 60 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", The intersection of history and mathematics, Science Networks Historical Studies, vol. 15, Basel, Boston, Berlin: Birkhäuser, pp. 51–66, 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, ISSN 0315-0860, MR 0469635

archive.org

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
Lang 1987a, Ch. XVI.6 Lang, Serge (1987a), Calculus of several variables (3rd ed.), Berlin, DE; New York, NY: Springer-Verlag, ISBN 978-0-387-96405-8
Lang 1987a, Ch. XVI.1 Lang, Serge (1987a), Calculus of several variables (3rd ed.), Berlin, DE; New York, NY: Springer-Verlag, ISBN 978-0-387-96405-8
Lang 1987a, Ch. XVI.5. For a more advanced, and more general statement see Lang 1969, Ch. VI.2 Lang, Serge (1987a), 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

books.google.com

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, Sam (1991), Theory of Matrices, Dover books on advanced mathematics, Courier Dover Corporation, p. 103, ISBN 978-0-486-66810-9.
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.
Mirsky 1990, Theorem 1.4.1 Mirsky, Leonid (1990), An Introduction to Linear Algebra, Courier Dover Publications, ISBN 978-0-486-66434-7
Needham, Joseph; Wang Ling (1959). Science and Civilisation in China. Vol. III. Cambridge: Cambridge University Press. p. 117. ISBN 978-0-521-05801-8.
Although many sources state that J. J. Sylvester coined the mathematical term "matrix" in 1848, Sylvester published nothing in 1848. (For proof that Sylvester published nothing in 1848, see J. J. Sylvester with H. F. Baker, ed., The Collected Mathematical Papers of James Joseph Sylvester (Cambridge, England: Cambridge University Press, 1904), vol. 1.) His earliest use of the term "matrix" occurs in 1850 in 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 ... "
The Collected Mathematical Papers of James Joseph Sylvester: 1837–1853, Paper 37, p. 247

britannica.com

"Matrix | mathematics". Encyclopedia Britannica. Retrieved 2020-08-19.

doi.org

Grcar, Joseph F. (2011-01-01). "John von Neumann's Analysis of Gaussian Elimination and the Origins of Modern Numerical Analysis". SIAM Review. 53 (4): 607–682. doi:10.1137/080734716. ISSN 0036-1445.
Perrone (2024), pp. 99–100 Perrone, Paolo (2024), Starting Category Theory, World Scientific, doi:10.1142/9789811286018_0005, ISBN 978-981-12-8600-1
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
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, ISSN 0315-0860, MR 0469635

kth.se

system.nada.kth.se

"A matrix having at least one dimension equal to zero is called an empty matrix", MATLAB Data Structures Archived 2009-12-28 at the Wayback Machine

loc.gov

lccn.loc.gov

Nering (1970, p. 37) Nering, Evar D. (1970), Linear Algebra and Matrix Theory (2nd ed.), New York: Wiley, LCCN 76-91646
Bronson (1970, p. 16) Bronson, Richard (1970), Matrix Methods: An Introduction, New York: Academic Press, LCCN 70097490
Protter & Morrey (1970, p. 869) Protter, Murray H.; Morrey, Charles B. Jr. (1970), College Calculus with Analytic Geometry (2nd ed.), Reading: Addison-Wesley, LCCN 76087042

mathsisfun.com

"How to Multiply Matrices". www.mathsisfun.com. Retrieved 2020-08-19.

merriam-webster.com

Merriam-Webster dictionary, Merriam-Webster, retrieved April 20, 2009

omatrix.com

"Empty Matrix: A matrix is empty if either its row or column dimension is zero", Glossary Archived 2009-04-29 at the Wayback Machine, O-Matrix v6 User Guide

siam.org

epubs.siam.org

Grcar, Joseph F. (2011-01-01). "John von Neumann's Analysis of Gaussian Elimination and the Origins of Modern Numerical Analysis". SIAM Review. 53 (4): 607–682. doi:10.1137/080734716. ISSN 0036-1445.

umich.edu

quod.lib.umich.edu

Kronecker 1897 Kronecker, Leopold (1897), Hensel, Kurt (ed.), Leopold Kronecker's Werke, Teubner
Weierstrass 1915, pp. 271–286 Weierstrass, Karl (1915), Collected works, vol. 3

web.archive.org

Press, Flannery & Teukolsky et al. 1992 Press, William H.; Flannery, Brian P.; Teukolsky, Saul A.; Vetterling, William T. (1992), "LU Decomposition and Its Applications" (PDF), Numerical Recipes in FORTRAN: The Art of Scientific Computing (2nd ed.), Cambridge University Press, pp. 34–42, archived from the original on 2009-09-06
"Empty Matrix: A matrix is empty if either its row or column dimension is zero", Glossary Archived 2009-04-29 at the Wayback Machine, O-Matrix v6 User Guide
"A matrix having at least one dimension equal to zero is called an empty matrix", MATLAB Data Structures Archived 2009-12-28 at the Wayback Machine

wolfram.com

mathworld.wolfram.com

Weisstein, Eric W. "Matrix". mathworld.wolfram.com. Retrieved 2020-08-19.

worldcat.org

search.worldcat.org

Grcar, Joseph F. (2011-01-01). "John von Neumann's Analysis of Gaussian Elimination and the Origins of Modern Numerical Analysis". SIAM Review. 53 (4): 607–682. doi:10.1137/080734716. ISSN 0036-1445.
Coburn 1955, Ch. V Coburn, Nathaniel (1955), Vector and tensor analysis, New York, NY: Macmillan, OCLC 1029828
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, ISSN 0315-0860, MR 0469635

worldscientific.com

Perrone (2024), pp. 99–100 Perrone, Paolo (2024), Starting Category Theory, World Scientific, doi:10.1142/9789811286018_0005, ISBN 978-981-12-8600-1