Positive-definite kernel

<p>In <a href="/facts/Operator_theory/Ays1ofel">operator theory</a>, a branch of mathematics, a positive-definite kernel is a generalization of a <a href="/facts/Positive-definite_function/RKqaCfp9">positive-definite function</a> or a <a href="/facts/Positive-definite_matrix/Hbr6AuPS">positive-definite matrix</a>. It was first introduced by <a href="/facts/James_Mercer_(mathematician)/Mvw2AHbU">James Mercer</a> in the early 20th century, in the context of solving <a href="/facts/Integral_equation/LCu4Imfq">integral operator equations</a>. Since then, positive-definite functions and their various analogues and generalizations have arisen in diverse parts of mathematics. They occur naturally in <a href="/facts/Fourier_analysis/sUA8JP6q">Fourier analysis</a>, <a href="/facts/Probability_theory/mFBn51rE">probability theory</a>, <a href="/facts/Operator_theory/Ays1ofel">operator theory</a>, <a href="/facts/Complex_analysis/hgCoQlH0">complex function-theory</a>, <a href="/facts/Moment_problem/bB3omnsy">moment problems</a>, <a href="/facts/Integral_equation/LCu4Imfq">integral equations</a>, <a href="/facts/Boundary_value_problem/QEfmUqmP">boundary-value problems</a> for <a href="/facts/Partial_differential_equation/DyPsBlv7">partial differential equations</a>, <a href="/facts/Machine_learning/e0w0XJTu">machine learning</a>, <a href="/facts/Embedding_problem/3t8mfRhE">embedding problem</a>, <a href="/facts/Information_theory/qNLH3U5P">information theory</a>, and other areas.
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Positive-definite kernel open-in-new

Positive-definite kernel