Kernel

1. The kernel is the essential part of a seed; all that is within the seed walls; the edible substance contained in the shell of a nut; hence, anything included in a shell, husk, or integument; as, the kernel of a nut. Also a single seed or grain; as, a kernel of corn.

2. The kernel is the essential part of an operating system. It is generally responsible for resource allocation, low-level hardware interfaces, security, and so forth. Some operating systems have a great deal of functionality implemented in the kernel, a monolithic kernel; others have a microkernel which implements only a bare minimum, with the remaining features require small modules which can be flexibly configured. A monolithic kernel is much faster than a microkernel, though a microkernel can dynamically load and unload modules as needed to reduce resource usage. The Linux kernel is a good example of an open-source operating monolithic system kernel, the Windows NT kernel is an example of a more layered closed-source kernel design.

3. In mathematics, the kernel of a group homomorphism f : G -> H consists of all those elements of G which are sent by f to the identity element of H. The kernel forms a normal subgroup of G. Similar definitions are used for other types of homomorphisms: the kernel of a linear transformation A : V -> W consists of all those elements x of V for which A(x) = 0. The kernel is a subspace of the vector space V. The situation of an homomorphism between modules is analogous. The kernel of a ring homomorphism f : R -> S consists of all those elements x of R for which f(x) = 0. Such a kernel is always an ideal of R.