Sylvester's law of inertia

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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

SAS^T

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

• Metric signature

[edit] External links

• Sylvester's law on PlanetMath.
• The original 1852 statement and proof of Sylvester's law of inertia.