The concept of kernel is everywhere:

Here’s a comparison of the various contexts in which the term “kernel” is used, organized in a table format:

Context	Definition	Functionality	Common Characteristics
GPU Computing	A function executed in parallel on the GPU.	Performs data processing tasks efficiently using parallelism.	Written in CUDA/OpenCL, optimized for large datasets.
Linear Algebra	The set of vectors mapped to zero by a linear transformation.	Helps understand the structure and properties of linear transformations.	Fundamental to linear maps, defined for vector spaces.
Python	An execution environment for running code (e.g., in Jupyter notebooks).	Executes code interactively, allowing real-time feedback.	Supports multiple languages, communicates with UI for execution.
Homology	A concept in algebraic topology related to cycles and boundaries.	Captures topological features of spaces through algebraic structures.	Involves boundary operators, identifies cycles in topological spaces.
Machine Learning	Functions that compute similarity between data points in high-dimensional space.	Enables kernelized algorithms like Support Vector Machines (SVM).	Includes various types of kernel functions (e.g., linear, polynomial, RBF).
Operating Systems	The core component of an operating system managing resources and communication between hardware and software.	Handles memory management, process scheduling, and device control.	Central to system operations, manages interactions between software and hardware.
Image Processing	A small matrix used to apply effects (e.g., blurring, sharpening) in image convolution operations.	Modifies pixel values based on surrounding pixels for various effects.	Defines how local areas of an image are transformed, essential for many image filters.
Statistics	A function used in non-parametric methods to estimate probability density functions.	Estimates the underlying probability distribution of a dataset.	Defines the influence of each data point on density estimates, often Gaussian or Epanechnikov.
Functional Analysis	A function defining an integral operator in functional analysis.	Transforms input functions into output functions via integration.	Represents mathematical transformations in functional spaces.
Graph Theory	A set of vertices in a directed graph that are independent and adjacent to other vertices.	Used in optimization problems and graph algorithms.	Helps identify independent sets within graph structures, crucial for graph theory applications.
Neural Networks	Filters (or convolution kernels) used in convolutional neural networks to extract features from input data.	Captures local patterns in data, particularly in image recognition tasks.	Involves sliding operations over input data to extract features, fundamental to CNNs.
Physics and Engineering	A mathematical function or operator describing interactions in quantum field theory.	Models interactions and propagations within a physical field.	Central to understanding interactions in theoretical physics, often tied to integral equations.

Summary

The term “kernel” spans various fields, and while the specific definitions and functionalities differ, the underlying concepts of centrality, transformation, and functional relevance are consistent across these contexts. Each kernel serves a fundamental role in its respective domain, whether in computation, analysis, or theoretical frameworks.

The fundamental essence of kernels should be pivoting on the definition of “kernel” as a “space or object mapped to a null space,” we see a common theme across various contexts: kernels serve as mechanisms for filtering, transforming, or optimizing data, relationships, or processes.