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 real...

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

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

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...

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

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

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

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

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

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

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

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

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

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...

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

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

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

{\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...

algebraic function over an algebraic domain is known as a period. The following is a list of some of the most common or interesting definite integrals...

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

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...

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...

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

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...