Sylvester's theorem

Sylvester's theorem or the Sylvester theorem may refer to any of several theorems named after James Joseph Sylvester: The Weinstein–Aronszajn identity, stating that det(I + AB) = det(I + BA), for matrices A, B, is sometimes attributed to 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 length