Sylvester's inertia law states that 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
 |
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.
