Sylvester's law of inertia
From Wikipedia, the free encyclopedia
In linear algebra, Sylvester's law of inertia states that the inertia of a symmetric matrix A is invariant under congruence transformations. It is named for J. J. Sylvester.
The inertia of a symmetric matrix A is defined as the triple containing the numbers of positive, negative and zero eigenvalues of A: see also signature (quadratic form). A congruence transformation of A is formed as the product
- SAST
where S is any given non-singular matrix. In other words, the signature of A as quadratic form is well-defined and independent under congruence transformations.
[edit] See also
[edit] External links
- Sylvester's law on PlanetMath.
- The original 1852 statement and proof of Sylvester's law of inertia.
