In mathematics, a positive-definite function is, depending on the context, either of two types of function. Let R {\displaystyle \mathbb {R} } be the set...

positive-definite. See, in particular: Positive-definite bilinear form Positive-definite function Positive-definite function on a group Positive-definite functional...

branch of mathematics, a positive-definite kernel is a generalization of a positive-definite function or a positive-definite matrix. It was first introduced...

with real entries is positive-definite if the real number   x ⊤ M x   {\displaystyle \ \mathbf {x} ^{\top }M\mathbf {x} \ } is positive for every nonzero...

and specifically in operator theory, a positive-definite function on a group relates the notions of positivity, in the context of Hilbert spaces, and...

that sign, the quadratic form is called positive-definite or negative-definite. A semidefinite (or semi-definite) quadratic form is defined in much the...

Lyapunov-candidate-function V {\displaystyle V} is locally positive definite, and the time derivative of the Lyapunov-candidate-function is locally negative definite: V...

representation of a symmetric positive-definite function on a square as a sum of a convergent sequence of product functions. This theorem, presented in...

distribution. The probability density function of the symmetric generalized normal distribution is a positive-definite function for β ∈ ( 0 , 2 ] {\displaystyle...

_{r\rightarrow \infty }\alpha (r)=\infty } . A nondecreasing positive definite function β {\displaystyle \beta } satisfying all conditions of class K...

Fourier transform a continuous positive-definite function on a locally compact abelian group corresponds to a finite positive measure on the Pontryagin dual...

mathematics, positive semidefinite may refer to: Positive semidefinite function Positive semidefinite matrix Positive semidefinite quadratic form Positive semidefinite...

non-singular is exactly the definition of a strictly positive definite function. Such functions, including the Gaussian, inverse quadratic, and inverse...

Constantin Carathéodory in terms of the positive definiteness of their Taylor coefficients. A positive function f on the unit disk with f(0) = 1 is harmonic...

symmetric and positive definiteness follows from the properties of inner product in F {\displaystyle F} . Conversely, every positive definite function and corresponding...

Bernoulli, the gamma function Γ ( z ) {\displaystyle \Gamma (z)} is defined for all complex numbers z {\displaystyle z} except non-positive integers, and for...

of a given real number is positive or negative, or the given number is itself zero. In mathematical notation the sign function is often represented as sgn...

degree 3. {\displaystyle 3.} The Hessian matrix of a convex function is positive semi-definite. Refining this property allows us to test whether a critical...

of calculus relates definite integration to differentiation and provides a method to compute the definite integral of a function when its antiderivative...

of almost periodic functions, positive-definite functions, derivatives, and convolution. Shifts of sequences (functions of an integer variable) appear...

{K}}_{\infty }} , χ ∈ K {\displaystyle \chi \in {\mathcal {K}}} and positive-definite function α {\displaystyle \alpha } , such that: ψ 1 ( | x | ) ≤ V ( x )...

particularly in functional analysis, a seminorm is a norm that need not be positive definite. Seminorms are intimately connected with convex sets: every seminorm...

= C {\displaystyle C^{\mathsf {T}}=C} , and positive-definite. The following integrals with this function can be calculated with the same technique: ∫...

Positive-real functions, often abbreviated to PR function or PRF, are a kind of mathematical function that first arose in electrical network synthesis...

/4}{\sqrt {2\pi }})^{N}} for any positive-definite symmetric matrix A {\displaystyle A} . Suppose A is a symmetric positive-definite (hence invertible) n × n...

(pronounced /ʃəˈlɛski/ shə-LES-kee) is a decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate...

These radial basis functions are from C ∞ ( R ) {\displaystyle C^{\infty }(\mathbb {R} )} and are strictly positive definite functions that require tuning...

theorem Plancherel's theorem Convolution Convolution theorem Positive-definite function Poisson summation formula Paley-Wiener theorem Sobolev space Time–frequency...

is a special function on the complex plane. It is defined as one particular definite integral of the ratio between an exponential function and its argument...

Differentialquotienten" (Mr. Weierstrass read [a paper] about continuous functions without definite [i.e., well-defined] derivatives [to members of the Academy])...