Negative definiteness information

mathematics, negative definiteness is a property of any object to which a bilinear form may be naturally associated, which is negative-definite. See, in particular:...

nonnegative). Negative-definite and negative semi-definite matrices are defined analogously. A matrix that is not positive semi-definite and not negative semi-definite...

involving products of two different variables. Positive or negative-definiteness or semi-definiteness, or indefiniteness, of this quadratic form is equivalent...

the signs of these minors are the conditions for the positive or negative definiteness of the Hessian. For the general case of an arbitrary number n of...

In quantum mechanics, counterfactual definiteness (CFD) is the ability to speak "meaningfully" of the definiteness of the results of measurements that...

a compact Lie group. The definition of compactness in terms of negative definiteness of the Killing form is more restrictive, since using this definition...

positive-definite at x , {\displaystyle x,} then f {\displaystyle f} attains an isolated local minimum at x . {\displaystyle x.} If the Hessian is negative-definite...

AFF) and negation (NEG) are ways in which grammar encodes positive and negative polarity into verb phrases, clauses, or other utterances. An affirmative...

positive definite if q(v) > 0 (similarly, negative definite if q(v) < 0) for every nonzero vector v. When q(v) assumes both positive and negative values...

{V}\cdot g} is locally positive definite, or ∇ V ⋅ g {\displaystyle \nabla {V}\cdot g} is locally negative definite. Lyapunov functions arise in the...

completely defines the process' behaviour. Importantly the non-negative definiteness of this function enables its spectral decomposition using the Karhunen–Loève...

orthogonal subspaces A and B, X = A + B, where q is positive-definite on A and negative-definite on B. The null cone, or isotropic cone, of X consists of...

number, definiteness and case. Pronouns are classified as: personal, possessive, interrogative, demonstrative, reflexive, universal, negative, indefinite...

non-negative definite and bounded: 0 ≤ Q ( α ) ≤ 1 π . {\displaystyle 0\leq Q(\alpha )\leq {\frac {1}{\pi }}.} Despite the fact that Q is non-negative definite...

one-dimensional subspace, and a complementary subspace on which it is negative definite. In a more formal statement, specify that V is a non-singular projective...

and only if q is a definite form: either q is positive definite, i.e. q(v) > 0 for all non-zero v in V; or q is negative definite, i.e. q(v) < 0 for all...

Cl0,n(R), depending on whether the author prefers positive-definite or negative-definite spaces. A standard basis {e1, ..., en} for Rp,q consists of...

vector subspace on which the scalar product g is positive-definite (resp. negative-definite), and r is the dimension of the radical of the scalar product...

eigenvalues are real. A symmetric n×n-matrix is called positive-definite (respectively negative-definite; indefinite), if for all nonzero vectors x ∈ R n {\displaystyle...

{\displaystyle p} on which the Hessian of f {\displaystyle f} is negative definite. The indices of basins, passes, and peaks are 0 , 1 , {\displaystyle...

Y')].} This is not necessarily non-negative, however. If ( M , d ) {\displaystyle (M,d)} is a strongly negative definite kernel, then D {\displaystyle D}...

of the outcome of an experiment is never negative, although a quasiprobability distribution allows a negative probability, or quasiprobability for some...

decomposition is that the Killing form is negative definite on k {\displaystyle {\mathfrak {k}}} and positive definite on p {\displaystyle {\mathfrak {p}}}...