kernel

A kernel is the core component of most computer operating systems. It serves as an intermediary between applications and hardware, providing essential services such as process and memory management, device drivers, file systems, networking, and security. The kernel runs with high privileges and enforces protection boundaries, enabling multitasking and efficient resource sharing while preventing user programs from directly manipulating hardware.

Kernel architectures vary. Monolithic kernels implement many services inside a single large address space, offering performance and simplicity (examples include Linux and traditional Unix). Microkernels minimize privileged code by running most services in user space and communicating via interprocess communication; real-world examples include QNX and other microkernel-inspired designs. Hybrid kernels blend approaches, combining a small core with in-kernel subsystems (as in Windows NT and modern macOS).

The term kernel also appears in mathematics. The kernel of a function is the set of inputs that map to a designated target, such as the identity in a group or zero in a vector space. For linear transformations, the kernel (null space) consists of vectors that map to zero; it is a subspace and its dimension relates to the rank by the rank-nullity theorem. In group theory, the kernel is the normal subgroup of elements mapped to the identity under a homomorphism.

In data science, a kernel function computes similarity by mapping data into a high-dimensional feature space without explicit transformation. This kernel trick enables algorithms such as support vector machines and kernel ridge regression. Common kernels include linear, polynomial, radial basis function (Gaussian), and sigmoid.