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–Gallai configuration, a set of points and lines without any two-point lines
Sylvester matroid, a matroid without any two-point lines.
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
