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 in variables is reduced by a nonsingular linear transformation to the form
Sylvester's Inertia Law
See alsoEigenvalue, Quadratic Form
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ReferencesGradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 6th ed. San Diego, CA: Academic Press, p. 1062, 2000.
Referenced on Wolfram|AlphaSylvester's Inertia Law
Cite this as:
Weisstein, Eric W. "Sylvester's Inertia Law." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SylvestersInertiaLaw.html