Sylvester's Inertia Law
The numbers of Eigenvalues that are Positive, Negative, or 0 do not change under a congruencetransformation. Gradshteyn and Ryzhik (1979) state it as follows: when a Quadratic Form 
in 
variables is reducedby a nonsingular linear transformation to the form
the number
of Positive Squares appearing in the reduction is an invariant of theQuadratic Form and does not depend on the method of reduction.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.
- Functional
- Functional Analysis
- Functional Calculus
- Functional Derivative
- Function Field
- Function Space
- Functor
- Fundamental Class
- Fundamental Continuity Theorem
- Fundamental Discriminant
- Fundamental Forms
- Fundamental Group
- Fundamental Homology Class
- Fundamental Lemma of Calculus of Variations
- Fundamental System
- Fundamental Theorem of Algebra
- Fundamental Theorem of Arithmetic
- Fundamental Theorem of Curves
- Fundamental Theorem of Directly Similar Figures
- Fundamental Theorem of Gaussian Quadrature
- Fundamental Theorem of Genera
- Fundamental Theorem of Plane Curves
- Fundamental Theorem of Projective Geometry
- Fundamental Theorem of Space Curves
- Fundamental Theorem of Symmetric Functions