kernel🔊

The core, center, or essence of an object or system. +

(botany) The central (usually edible) part of a nut, especially once the hard shell has been removed.

(botany) A single seed or grain, especially of corn or wheat.

(US) The stone of certain fruits, such as peaches or plums.

A small mass around which other matter is concreted; a nucleus; a concretion or hard lump in the flesh.

(computing) The central part of many computer operating systems which manages the system's resources and the communication between hardware and software components.

(computing) The core engine of any complex software system.

(programming) The simplified input to an algorithm that has undergone kernelization.

(calculus) A function used to define an integral transform.

(settheoretickernel) (of a function f) The set of pairs of elements in the domain of f which are mapped to the same value; the equivalence relation x\equiv y\iff f(x)=f(y).

(of a morphism f between algebraic structures) The set of elements of the domain of f which are mapped to an identity element.

(of a group homomorphism f\colon G\to H between groups) The set of elements of G which are mapped to the identity of H (usually written as 0 in an additive group and as 1 in a multiplicative group).

(of a ring homomorphism f\colon R\to S between rings) The set of elements of R which are mapped to the additive identity 0 of S.

(of a linear transformation f\colon M\to N between modules or vector spaces) The set of elements of M which are mapped to the additive identity 0 of N.

(of a morphism f: X\to Y in a category with zero morphisms) The equalizer of f and the zero morphism from X to Y, denoted \operatorname{ker}f.

(category theory) The source of \operatorname{ker}f, denoted \operatorname{Ker}f.

(fuzzy set theory) The set of members of a fuzzy set that are fully included (i.e., whose grade of membership is 1).

(slang) The human clitoris.

(chemistry) The nucleus and electrons of an atom excluding its valence electrons.

To enclose within a kernel

To crenellate