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

the number of Positive Squares appearing in the reduction is an invariant of the Quadratic Form and does not depend on the method of reduction.

**References**

Gradshteyn, I. S. and Ryzhik, I. M. *Tables of Integrals, Series, and Products, 5th ed.* San Diego, CA:
Academic Press, p. 1105, 1979.

© 1996-9

1999-05-26