List of things named after James Joseph Sylvester
The mathematician J. J. Sylvester was known for his ability to coin new names and new notation for mathematical objects, not based on his own name. Nevertheless, many objects and results in mathematics have come to be named after him:
- The Sylvester–Gallai theorem, on the existence of a line with only two of n given points.
- Sylvester's determinant identity, stating that det(I + AB) = det(I + BA), for matrices A, B.
- 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
- 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
Other things named after Sylvester
- Sylvester (crater), an impact crater on the moon
- Sylvester Medal, given by the Royal Society for the encouragement of mathematical research
- 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
- 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 1557527.
- 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, doi:10.1007/BF02112289.
- 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 0255432.
- 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", British Journal for the History of Science, 37 (1(132)): 75–92, doi:10.1017/S0007087403005132, MR 2128208