• The Sylvester–Gallai theorem
  Sylvester–Gallai theorem
  The Sylvester–Gallai theorem asserts that given a finite number of points in the Euclidean plane, either# all the points are collinear; or# there is a line which contains exactly two of the points.This claim was posed as a problem by...
  
  , on the existence of a line with only two of n given points.
• Sylvester's determinant theorem
  Sylvester's determinant theorem
  In matrix theory, Sylvester's determinant theorem is a theorem useful for evaluating certain types of determinants. It is named after James Joseph Sylvester....
  
  , stating that det(I + AB) = det(I + BA), for matrices A, B.
• Sylvester's matrix theorem, a.k.a. Sylvester's formula
  Sylvester's formula
  In matrix theory, Sylvester's formula or Sylvester's matrix theorem expresses an analytic function f of a matrix A in terms of the eigenvalues and eigenvectors of A...
  
  , 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
  Sylvester's law of inertia
  Sylvester's law of inertia is a theorem in matrix algebra about certain properties of the coefficient matrix of a real quadratic form that remain invariant under a change of coordinates...
  
   a.k.a. Sylvester's rigidity theorem, about the signature of a quadratic form.
• Sylvester's identity about determinants of submatrices
• Sylvester's criterion
  Sylvester's criterion
  In mathematics, Sylvester’s criterion is a necessary and sufficient criterion to determine whether a Hermitian matrix is positive-definite. It is named after James Joseph Sylvester....
  
  , a characterization of positive-definite Hermitian matrices.
• The Sylvester matrix
  Sylvester matrix
  In mathematics, a Sylvester matrix is a matrix associated to two polynomials that provides information about those polynomials. It is named for James Joseph Sylvester.-Definition:...
  
   for two polynomials.
• Sylvester's sequence
  Sylvester's sequence
  In number theory, Sylvester's sequence is an integer sequence in which each member of the sequence is the product of the previous members, plus one. The first few terms of the sequence are:...
  
  , where each term is the product of previous terms plus one.
• Sylvester cyclotomic numbers.
• The Sylvester equation
  Sylvester equation
  The Sylvester equation, commonly encountered in control theory, is the matrix equation of the formA X + X B = C,where A,B,X,C are n \times n matrices. A,B,C are known...
  
  , 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
  Greedy algorithm for Egyptian fractions
  In mathematics, the greedy algorithm for Egyptian fractions is a greedy algorithm, first described by Fibonacci, for transforming rational numbers into Egyptian fractions. An Egyptian fraction is a representation of an irreducible fraction as a sum of unit fractions, as e.g. 5/6 = 1/2 + 1/3...
  
   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.

Other things named after Sylvester

• Sylvester (crater)
  Sylvester (crater)
  Sylvester is a lunar impact crater that is located near the north pole of the Moon, along the northern limb in the libration zone. It lies just to the south-southeast of the craters Grignard and Hermite; the latter of which is within one crater diameter of the pole. South of Sylvester is Pascal...
  
  , an impact crater on the moon
• Sylvester Medal
  Sylvester Medal
  The Sylvester Medal is a bronze medal awarded by the Royal Society for the encouragement of mathematical research, and accompanied by a £1,000 prize...
  
  , given by the Royal Society for the encouragement of mathematical research

See also

• Sylvester's closed solution for the Frobenius coin problem
  Coin problem
  The coin problem is a mathematical problem that asks what is the largest monetary amount that cannot be obtained using only coins of specified denominations. For example, the largest amount that cannot be obtained using only coins of 3 and 5 units is 7 units...
  
   when there are only two coins.
• Sylvester's construction for an arbitrarily large Hadamard matrix
  Hadamard matrix
  In mathematics, an Hadamard matrix, named after the French mathematician Jacques Hadamard, is a square matrix whose entries are either +1 or −1 and whose rows are mutually orthogonal...
  
  .

• Scientific equations named after people
  Scientific equations named after people
  This is a list of scientific equations named after people .-See also:* Eponym* List of eponymous laws* List of laws in science* List of equations* Scientific constants named after people* Scientific phenomena named after people...