Sylvester's theorem
Introduction '''Sylvester's theorem''' or '''the Sylvester theorem''' may refer to any of several theorems named after James Joseph Sylvester:* The Sylvester–Gallai theorem, on the existence of a line with only two of ''n'' given points. * Sylvester's determinant identity. * Sylvester's matrix theorem, also called Sylvester's formula, for a matrix function in terms of eigenvalues. * Sylvester's law of inertia, also called Sylvester's rigidity theorem, about the signature of a quadratic form. * Sylvester's theorem on the product of ''k'' consecutive integers > ''k'', that generalizes Bertrand's postulate. * Sylvester's theorem on partitions. * Sylvester theorem on spherical harmonics. * Sylvester's criterion, a characterization of positive-definite Hermitian matrices. * Sylvester’s inequality about the rank (linear algebra) of the product of two matrices. * Sylvester's closed solution for the Frobenius coin problem when there are only two coins. * Sylvester's triangle problem, a particular geometric representation of the sum of three vectors of equal lengthThe Weinstein–Aronszajn identity, stating that det(''I'' + ''AB'') = det(''I'' + ''BA''), for matrices ''A'', ''B'', is sometimes attributed to Sylvester.
See also *List of topics named after James Joseph Sylvester