The numbers of Eigenvalues that are Positive, Negative, or 0 do not change under a congruence
transformation. Gradshteyn and Ryzhik (1979) state it as follows: when a Quadratic Form in variables is reduced
by a nonsingular linear transformation to the form
See also Eigenvalue, Quadratic Form
References
Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 5th ed. San Diego, CA:
Academic Press, p. 1105, 1979.