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Sylvester's theorem
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 theorem, stating that det(''I'' + ''AB'') = det(''I'' + ''BA''), for matrices ''A'', ''B''.
* 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.
It may also refer to the following theorems proved by J. J. Sylvester:
* 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.
==See also==
*List of topics named after James Joseph Sylvester
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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