List of things named after James Joseph Sylvester

• 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
• 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 + rank − n ≤ rank 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, an impact crater on the moon
• Sylvester Medal, given by the Royal Society for the encouragement of mathematical research
• , a vector, matrix and geometry library for JavaScript