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.
- Odd Sequence
- ODE
- Offset Rings
- Ogive
- Oldknow Points
- Omega Constant
- Omega Function
- Omino
- Omnific Integer
- O'Nan Group
- Onduloid
- One
- One-Form
- One-Mouth Theorem
- One-Ninth Constant
- One-to-One
- One-Way Function
- Only Critical Point in Town Test
- Onto
- Open Disk
- Open Interval
- Open Map
- Open Mapping Theorem
- Open Set
- Operad