# positive definite kernel

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*English-Chinese computer dictionary (英汉计算机词汇大词典).
2013.*

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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**Kernel**— may refer to:Computing* Kernel (computer science), the central component of most operating systems ** Linux kernel * Kernel (programming language), a Scheme like language * kernel trick, in machine learningLiterature* Kernel ( Lilo Stitch ),… … Wikipedia**Kernel (mathematics)**— In mathematics, the word kernel has several meanings. Kernel may mean a subset associated with a mapping:* The kernel of a mapping is the set of elements that map to the zero element (such as zero or zero vector), as in kernel of a linear… … Wikipedia**Kernel trick**— In machine learning, the kernel trick is a method for using a linear classifier algorithm to solve a non linear problem by mapping the original non linear observations into a higher dimensional space, where the linear classifier is subsequently… … 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**Multivariate kernel density estimation**— Kernel density estimation is a nonparametric technique for density estimation i.e., estimation of probability density functions, which is one of the fundamental questions in statistics. It can be viewed as a generalisation of histogram density… … Wikipedia**Mercer's theorem**— In mathematics, specifically functional analysis, Mercer s theorem is a representation of a symmetric positive definite function on a square as a sum of a convergent sequence of product functions. This theorem, presented in (Mercer 1909), is one… … Wikipedia**Bochner's theorem**— In mathematics, Bochner s theorem characterizes the Fourier transform of a positive finite Borel measure on the real line. Background Given a positive finite Borel measure μ on the real line R, the Fourier transform Q of μ is the continuous… … Wikipedia**List of mathematics articles (P)**— NOTOC P P = NP problem P adic analysis P adic number P adic order P compact group P group P² irreducible P Laplacian P matrix P rep P value P vector P y method Pacific Journal of Mathematics Package merge algorithm Packed storage matrix Packing… … Wikipedia