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Sylvester's Inertia Law

  • Definition: 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 Q=y_1^2+y_2^2+...+y_p^2-y_(p+1)^2-y_(p_2)^2-...-y_r^2, 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.

    Source: http://mathworld.wolfram.com

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