- In mathematics, a
degenerate case is a
limiting case of a
class of
objects which appears to be
qualitatively different from (and
usually simpler than)...
- The most
important examples of
nondegenerate forms are
inner products and
symplectic forms.
Symmetric nondegenerate forms are
important generalizations...
-
injective (hence "
nondegenerate" in the
above sense) but not unimodular. For example, over the integers, the
pairing B(x, y) = 2xy is
nondegenerate but not unimodular...
- In mathematics, a real
interval is the set of all real
numbers lying between two
fixed endpoints with no "gaps". Each
endpoint is
either a real number...
-
called nondegenerate; this
includes positive definite,
negative definite, and
isotropic quadratic form (a mix of 1 and −1); equivalently, a
nondegenerate quadratic...
-
spaces if they have an
inner product (or more
generally a
symmetric nondegenerate form) and an orientation; this is less data than an
isomorphism to Euclidean...
- is a
differentiable manifold with a
metric tensor that is
everywhere nondegenerate. This is a
generalization of a
Riemannian manifold in
which the requirement...
- On an
inner product space, or more
generally a
vector space with a
nondegenerate form (hence an
isomorphism V → V ∗ {\displaystyle V\to V^{*}} ), vectors...
- the
theory of
nondegenerate quadratic forms on
vector spaces, the finite-dimensional real and
complex Clifford algebras for a
nondegenerate quadratic form...
-
vector space spanned by its rows. Rank is thus a
measure of the "
nondegenerateness" of the
system of
linear equations and
linear transformation encoded...
