The mathematician J. J. Sylvester was known for his ability to coin new names and new notation for mathematical objects,[1] not based on his own name. Nevertheless, many objects and results in mathematics have come to be named after him:[2]
- The Sylvester–Gallai theorem, on the existence of a line with only two of n given points.[3]
- Sylvester–Gallai configuration, a set of points and lines without any two-point lines.
- Sylvester matroid, a matroid without any two-point lines.[4]
- Sylvester's determinant identity.
- Sylvester's matrix theorem, a.k.a. Sylvester's formula, for a matrix function in terms of eigenvalues.
- Sylvester's theorem on the product of k consecutive integers > k, that generalizes Bertrand's postulate.
- Sylvester's law of inertia a.k.a. Sylvester's rigidity theorem, about the signature of a quadratic form.
- Sylvester's identity about determinants of submatrices.[5]
- Sylvester's criterion, a characterization of positive-definite Hermitian matrices.
- Sylvester domain.
- The Sylvester matrix for two polynomials.
- Sylvester's sequence, where each term is the product of previous terms plus one.
- Sylvester cyclotomic numbers.
- The Sylvester equation, AX XB = C where A, B, C are given matrices and X is an unknown matrix.
- Sylvester's "four point problem" of geometric probability.
- The Sylvester expansion or Fibonacci–Sylvester expansion of a rational number, a representation as a sum of unit fractions found by a greedy algorithm.
- Sylvester's rank inequality rank(A) rank(B) − n ≤ rank(AB) on the rank of the product of an m × n matrix A and an n × p matrix B.
- Sylver coinage, a number-theoretic game.[6]
- Sylvester's bijection, a correspondence between partitions into distinct and odd parts.
Other things named after Sylvester
edit- Sylvester (crater), an impact crater on the Moon
- Sylvester Medal, given by the Royal Society for the encouragement of mathematical research[7]
- Sylvester (javascript library), a vector, matrix and geometry library for JavaScript
See also
edit- Sylvester's closed solution for the Frobenius coin problem when there are only two coins.
- Sylvester's construction for an arbitrarily large Hadamard matrix.
- Scientific equations named after people
References
edit- ^ Franklin, Fabian (1897), "James Joseph Sylvester", Bulletin of the American Mathematical Society, 3 (9): 299–309, doi:10.1090/S0002-9904-1897-00424-4, MR 1557527299-309&rft.date=1897&rft_id=info:doi/10.1090/S0002-9904-1897-00424-4&rft_id=https://mathscinet.ams.org/mathscinet-getitem?mr=1557527#id-name=MR&rft.aulast=Franklin&rft.aufirst=Fabian&rfr_id=info:sid/en.wikipedia.org:List of things named after James Joseph Sylvester" class="Z3988">.
- ^ MathSciNet lists over 500 mathematics articles with "Sylvester" in their titles, most of which concern mathematical subjects named after Sylvester.
- ^ Borwein, P.; Moser, W. O. J. (1990), "A survey of Sylvester's problem and its generalizations", Aequationes Mathematicae, 40 (1): 111–135, CiteSeerX 10.1.1.218.8616, doi:10.1007/BF02112289, S2CID 122052678111-135&rft.date=1990&rft_id=https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.218.8616#id-name=CiteSeerX&rft_id=https://api.semanticscholar.org/CorpusID:122052678#id-name=S2CID&rft_id=info:doi/10.1007/BF02112289&rft.aulast=Borwein&rft.aufirst=P.&rft.au=Moser, W. O. J.&rfr_id=info:sid/en.wikipedia.org:List of things named after James Joseph Sylvester" class="Z3988">.
- ^ Murty, U. S. R. (1969), "Sylvester matroids", Recent Progress in Combinatorics (Proc. Third Waterloo Conf. on Combinatorics, 1968), New York: Academic Press, pp. 283–286, MR 0255432283-286&rft.pub=Academic Press&rft.date=1969&rft_id=https://mathscinet.ams.org/mathscinet-getitem?mr=0255432#id-name=MR&rft.aulast=Murty&rft.aufirst=U. S. R.&rfr_id=info:sid/en.wikipedia.org:List of things named after James Joseph Sylvester" class="Z3988">.
- ^ Erwin H. Bareiss (1968), Sylvester's Identity and Multistep Integer- Preserving Gaussian Elimination. Mathematics of Computation, Vol. 22, No. 103, pp. 565–578
- ^ Berlekamp, Elwyn R.; Conway, John H.; Guy, Richard K. (1982), "Sylver Coinage", Winning Ways for your Mathematical Plays, Vol. 2: Games in Particular, London: Academic Press Inc. [Harcourt Brace Jovanovich Publishers], pp. 576, 606, MR 0654502.
- ^ Cantor, Geoffrey (2004), "Creating the Royal Society's Sylvester Medal" (PDF), British Journal for the History of Science, 37 (1(132)): 75–92, doi:10.1017/S0007087403005132, MR 2128208, S2CID 14330716475-92&rft.date=2004&rft_id=https://mathscinet.ams.org/mathscinet-getitem?mr=2128208#id-name=MR&rft_id=https://api.semanticscholar.org/CorpusID:143307164#id-name=S2CID&rft_id=info:doi/10.1017/S0007087403005132&rft.aulast=Cantor&rft.aufirst=Geoffrey&rft_id=http://eprints.whiterose.ac.uk/3222/1/2004_bjhs_37_75-92.pdf&rfr_id=info:sid/en.wikipedia.org:List of things named after James Joseph Sylvester" class="Z3988">