List of things named after James Joseph Sylvester explained

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]

• The Sylvester–Gallai theorem, on the existence of a line with only two of n given points.^[3]
  • Sylvester–Gallai configuration, a set of points and lines without any two-point lines.
  • Sylvester matroid, a matroid without any two-point lines.^[4]
• 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.^[5]
• 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 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 matrix A and an matrix B.
• Sylver coinage, a number-theoretic game.^[6]

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 (javascript library), a vector, matrix and geometry library for JavaScript

See also

• 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

Notes and References

1. .
2. [MathSciNet]
3. .
4. .
5. Erwin H. Bareiss (1968), Sylvester's Identity and Multistep Integer- Preserving Gaussian Elimination. Mathematics of Computation, Vol. 22, No. 103, pp. 565 - 578
6. .