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...

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

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

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

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...

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

_{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...

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

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

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

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

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

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

nonnegative-definite matrix B, is concave. Rays bending in the computation of radiowave attenuation in the atmosphere involve concave functions. In expected...

{\displaystyle x\in A_{i}.} The definite integral of a step function is a piecewise linear function. The Lebesgue integral of a step function f = ∑ i = 0 n α i χ...

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

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

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

Scott, Evaluation of Classes of Definite Integrals Involving Elementary Functions via Differentiation of Special Functions, AAECC (Applicable Algebra in...

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

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

means that ∇ 2 f ( x ) − m I {\displaystyle \nabla ^{2}f(x)-mI} is positive semi-definite. This is equivalent to requiring that the minimum eigenvalue of...

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

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...

for which this is the case is called a period of the function. If there exists a least positive constant P with this property, it is called the fundamental...

terms of nth roots. If A is a positive-definite matrix or operator, then there exists precisely one positive definite matrix or operator B with B2 =...

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

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...