nondegenerate

The difference between the degenerate and nondegenerate cases has to do with the properties of the numbers involved.

This form will be nondegenerate if and only if A is an isomorphism.

Let Q be a real nondegenerate indefinite quadratic form in n variables.

One can check that the induced metric is nondegenerate and has Lorentzian signature.

For positive definiteness, take a nondegenerate representation of .

The lowest (hyperfine) energy level of H is nondegenerate.

In complex projective space all of the nondegenerate quadrics become indistinguishable from each other.

The most important examples of nondegenerate forms are inner products and symplectic forms.

Without loss of generality, one can assume that all balls in "'F"' are nondegenerate and have radius 1.

In this case B is nondegenerate.

Of these 16 forms, five are nondegenerate, and the remaining are degenerate forms.

If is semisimple and the underlying field has characteristic 0 , then is nondegenerate.

Because a symplectic form is nondegenerate, so is the associated bilinear form.

It has a nondegenerate signature.

For reference, Debye-Hückel screening describes the nondegenerate limit case.

A symplectic manifold is a manifold equipped with a closed, nondegenerate 2-form.

Most instances of geometric algebras of interest have a nondegenerate quadratic forms.

As above, we let (V, g) be an n-dimensional complex vector space equipped with a nondegenerate bilinear form.

If is nondegenerate, then is semisimple.

Suppose that V is a vector space with a nondegenerate bilinear form ( , ).

The most important Clifford algebras are those over real and complex vector spaces equipped with nondegenerate quadratic forms.

The notion of a Morse function can be generalized to consider functions that have nondegenerate manifolds of critical points.

Every nondegenerate triangle is strictly convex.

A Lie algebra is semisimple if and only if the Killing form is nondegenerate.

Berger then uses Brown's original form to present a simple and intuitive proof of convergence in the case of nondegenerate ordinal potential games.