Sylvester's Inertia Law

The numbers of eigenvalues that are positive, negative, or 0 do not change under a congruence transformation. Gradshteyn and Ryzhik (2000) state it as follows: when a quadratic form Q in n variables is reduced by a nonsingular linear transformation to the form


the number p of positive squares appearing in the reduction is an invariant of the quadratic form Q and does not depend on the method of reduction.

See also

Eigenvalue, Quadratic Form

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Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 6th ed. San Diego, CA: Academic Press, p. 1062, 2000.

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Sylvester's Inertia Law

Cite this as:

Weisstein, Eric W. "Sylvester's Inertia Law." From MathWorld--A Wolfram Web Resource.

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