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Kernel

Category
STANDARD MATHEMATICS
Definition
A function of two inputs used to encode pairwise relationships, integral operators or covariance-like structure.
Math Level
TECHNICAL

A kernel is a function of two inputs used to encode a relationship between them, often written K(x,y)K(x,y).

Evaluating a kernel on finitely many points produces a matrix. Positive-definite kernels are those for which these matrices satisfy the appropriate non-negative quadratic-form condition.

See also: matrix, positive definiteness, translation invariance, correlation..

Related glossary terms

  1. [..]CorrelationGLOSSARY · DSP
  2. [..]MatrixGLOSSARY · STANDARD MATHEMATICS
  3. [..]Positive definitenessGLOSSARY · STANDARD MATHEMATICS
  4. [..]Translation invarianceGLOSSARY · STANDARD MATHEMATICS

Read this term in context

  1. [..]Hilbert spaceARTICLE · ART-RC-0064
  2. [..]Inner productARTICLE · ART-RC-0063
  3. [..]MatrixARTICLE · ART-RC-0059
  4. [..]Quadratic formARTICLE · ART-RC-0058
  5. [..]Translation invarianceARTICLE · ART-RC-0062
  6. [..]What is positive definiteness?ARTICLE · ART-RC-0005