The mathematician
J. J. Sylvester
James Joseph Sylvester (3 September 1814 – 15 March 1897) was an English mathematician. He made fundamental contributions to matrix theory, invariant theory, number theory, partition theory, and combinatorics. He played a leadership ...
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
The Sylvester–Gallai theorem in geometry states that every finite set of points in the Euclidean plane has a line that passes through exactly two of the points or a line that passes through all of them. It is named after James Joseph Sylvester ...
, on the existence of a line with only two of ''n'' given points.
**
Sylvester–Gallai configuration In geometry, a Sylvester–Gallai configuration consists of a finite subset of the points of a projective space with the property that the line through any two of the points in the subset also passes through at least one other point of the subset.
...
, a set of points and lines without any two-point lines.
**
Sylvester matroid
In matroid theory, a Sylvester matroid is a matroid in which every pair of elements belongs to a three-element circuit (a ''triangle'') of the matroid..
Example
The n-point line (i.e., the rank 2 uniform matroid on n elements, U^2_n) is a Sylveste ...
, a matroid without any two-point lines.
*
Sylvester's determinant identity
In matrix theory, Sylvester's determinant identity is an identity useful for evaluating certain types of determinants. It is named after James Joseph Sylvester, who stated this identity without proof in 1851. Cited in
Given an ''n''-by-''n'' ma ...
.
*Sylvester's matrix theorem, a.k.a.
Sylvester's formula In matrix theory, Sylvester's formula or Sylvester's matrix theorem (named after J. J. Sylvester) or Lagrange−Sylvester interpolation expresses an analytic function of a matrix as a polynomial in , in terms of the eigenvalues and eigenvectors of ...
, for a matrix function in terms of eigenvalues.
*Sylvester's theorem on the product of ''k'' consecutive integers > ''k'', that generalizes
Bertrand's postulate
In number theory, Bertrand's postulate is a theorem stating that for any integer n > 3, there always exists at least one prime number p with
:n < p < 2n - 2.
A less restrictive formulation is: for every , there is always ...
.
*
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 number, real quadratic form that remain invariant (mathematics), invariant under a change of basis. Namely, if ''A'' is the symme ...
a.k.a. Sylvester's rigidity theorem, about the signature of a quadratic form.
*Sylvester's identity about determinants of submatrices.
*
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.
Sylvester's criterion states that a ''n'' × ''n'' Hermitian ma ...
, a characterization of positive-definite Hermitian matrices.
*
Sylvester domain In mathematics, a Sylvester domain, named after James Joseph Sylvester by , is a ring in which Sylvester's law of nullity holds. This means that if ''A'' is an ''m'' by ''n'' matrix, and ''B'' is an ''n'' by ''s'' matrix over ''R'', then
:ρ(''AB ...
.
*The
Sylvester matrix In mathematics, a Sylvester matrix is a matrix associated to two univariate polynomials with coefficients in a field or a commutative ring. The entries of the Sylvester matrix of two polynomials are coefficients of the polynomials. The determinant o ...
for two polynomials.
*
Sylvester's sequence
In number theory, Sylvester's sequence is an integer sequence in which each term of the sequence is the product of the previous terms, plus one. The first few terms of the sequence are
:2, 3, 7, 43, 1807, 3263443, 10650056950807, 11342371305542184 ...
, where each term is the product of previous terms plus one.
*
Sylvester cyclotomic numbers.
*The
Sylvester equation In mathematics, in the field of control theory, a Sylvester equation is a Matrix (mathematics), matrix equation of the form:
:A X + X B = C.
Then given matrices ''A'', ''B'', and ''C'', the problem is to find the possible matrices ''X'' that obey t ...
, ''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
Sylver coinage is a mathematical game for two players, invented by John H. Conway. It is discussed in chapter 18 of
'' Winning Ways for Your Mathematical Plays''. This article summarizes that chapter.
The two players take turns naming positive ...
, a number-theoretic game.
Other things named after Sylvester
*
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 d ...
, an impact crater on the moon
*
Sylvester Medal
The Sylvester Medal is a bronze medal awarded by the Royal Society (London) for the encouragement of mathematical research, and accompanied by a £1,000 prize. It was named in honour of James Joseph Sylvester, the Savilian Professor of Geometry a ...
, given by the Royal Society for the encouragement of mathematical research
a vector, matrix and geometry library for
JavaScript
JavaScript (), often abbreviated as JS, is a programming language that is one of the core technologies of the World Wide Web, alongside HTML and CSS. As of 2022, 98% of Website, websites use JavaScript on the Client (computing), client side ...
See also
*Sylvester's closed solution for the Frobenius
coin problem
The coin problem (also referred to as the Frobenius coin problem or Frobenius problem, after the mathematician Ferdinand Frobenius) is a mathematical problem that asks for the largest monetary amount that cannot be obtained using only coins of ...
when there are only two coins.
*Sylvester's construction for an arbitrarily large
Hadamard matrix
In mathematics, a 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. In geometric terms, this means that each pair of rows in ...
.
*
Scientific equations named after people
This is a list of scientific equations named after people (eponymous equations)."Reflections on the Natural History of Eponymy and Scientific Law", Donald deB. Beaver, ''Social Studies of Science'', volume 6, number 1 (February, 1976), pages 89–9 ...
References
{{reflist
Sylvester, J. J.