positive-definite space

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• Positive definite kernel — In operator theory, a positive definite kernel is a generalization of a positive matrix. Definition Let :{ H n } {n in {mathbb Z be a sequence of (complex) Hilbert spaces and :mathcal{L}(H i, H j)be the bounded operators from Hi to Hj . A map A… …   Wikipedia

• Positive definite function on a group — In operator theory, a positive definite function on a group relates the notions of positivity, in the context of Hilbert spaces, and algebraic groups. It can be viewed as a particular type of positive definite kernel where the underlying set has… …   Wikipedia

• Positive-definite matrix — In linear algebra, a positive definite matrix is a matrix that in many ways is analogous to a positive real number. The notion is closely related to a positive definite symmetric bilinear form (or a sesquilinear form in the complex case). The… …   Wikipedia

• Definite bilinear form — In mathematics, a definite bilinear form is a bilinear form B over some vector space V (with real or complex scalar field) such that the associated quadratic form is definite, that is, has a real value with the same sign (positive or negative)… …   Wikipedia

• 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

• Positive form — In complex geometry, the term positive form refers to several classes of real differential formsof Hodge type (p, p) . (1,1) forms Real ( p , p ) forms on a complex manifold M are forms which are of type ( p , p ) and real,that is, lie in the… …   Wikipedia

• Space — • The idea of space is one of the most important in the philosophy of the material world; for centuries it has preoccupied and puzzled philosophers and psychologists Catholic Encyclopedia. Kevin Knight. 2006. Space     Space …   Catholic encyclopedia

• Definite quadratic form — In mathematics, a definite quadratic form is a real valued quadratic form over some vector space V that has the same sign (always positive or always negative) for every nonzero vector of V. The definite quadratic forms correspond in one to one… …   Wikipedia

• Indefinite inner product space — In mathematics, in the field of functional analysis, an indefinite inner product space :(K, langle cdot,,cdot angle, J) is an infinite dimensional complex vector space K equipped with both an indefinite inner product :langle cdot,,cdot angle and… …   Wikipedia

• Inner product space — In mathematics, an inner product space is a vector space with the additional structure of inner product. This additional structure associates each pair of vectors in the space with a scalar quantity known as the inner product of the vectors.… …   Wikipedia

• Reproducing kernel Hilbert space — In functional analysis (a branch of mathematics), a reproducing kernel Hilbert space is a Hilbert space of functions in which pointwise evaluation is a continuous linear functional. Equivalently, they are spaces that can be defined by reproducing …   Wikipedia