- positive linear functional
-
A kind of linear functional which "returns" a non-negative scalar when "fed" a non-negative function as "parameter."
Wikipedia foundation.
positive linear functional
Look at other dictionaries:
Positive linear functional — In mathematics, especially in functional analysis, a positive linear functional on an ordered vector space ( V , ≤) is a linear functional f on V so that for all positive elements v of V , that is v ge;0, it holds that:f(v)geq 0.In other words, a … Wikipedia
Linear functional — This article deals with linear maps from a vector space to its field of scalars. These maps may be functionals in the traditional sense of functions of functions, but this is not necessarily the case. In linear algebra, a linear functional… … Wikipedia
Functional (mathematics) — In mathematics, a functional is traditionally a map from a vector space to the field underlying the vector space, which is usually the real numbers. In other words, it is a function that takes a vector as its argument or input and returns a… … Wikipedia
Functional integration — You may also be looking for functional integration (neurobiology) or functional integration (sociology). Functional integration is a collection of results in mathematics and physics where the domain of an integral is no longer a region of space,… … Wikipedia
Linear map — In mathematics, a linear map, linear mapping, linear transformation, or linear operator (in some contexts also called linear function) is a function between two vector spaces that preserves the operations of vector addition and scalar… … Wikipedia
Decomposition of spectrum (functional analysis) — In mathematics, especially functional analysis, the spectrum of an operator generalizes the notion of eigenvalues. Given an operator, it is sometimes useful to break up the spectrum into various parts. This article discusses a few examples of… … Wikipedia
List of functional analysis topics — This is a list of functional analysis topics, by Wikipedia page. Contents 1 Hilbert space 2 Functional analysis, classic results 3 Operator theory 4 Banach space examples … Wikipedia
State (functional analysis) — In functional analysis, a state on a C* algebra is a positive linear functional of norm 1. The set of states of a C* algebra A , sometimes denoted by S ( A ), is always a convex set. The extremal points of S ( A ) are called pure states. If A has … Wikipedia
Functional magnetic resonance imaging — Functional MRI or functional Magnetic Resonance Imaging (fMRI) is a type of specialized MRI scan. It measures the haemodynamic response related to neural activity in the brain or spinal cord of humans or other animals. It is one of the most… … Wikipedia
Positive — is a property of positivity and may refer to: Mathematics and science * Positive number, a number that is greater than 0 * Positive operator, in functional analysis, a bounded linear operator whose spectrum consists of positive real numbers *… … Wikipedia
