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]
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.
^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.
^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.
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Erwin H. Bareiss (1968), Sylvester's Identity and Multistep Integer- Preserving Gaussian Elimination. Mathematics of Computation, Vol. 22, No. 103, pp. 565–578
^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 143307164