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Different people want to reduce the size of the Linux kernel for different reasons. This page holds a few use cases for a small Linux kernel, as a means of illustrating some of the requirements and possibilities for this "feature" of the kernel.
Linux can be used on some devices at the primary bootloader. The size requirements on the first-stage bootloader are more stringent than for the ultimate running operating system.
There are projects along these lines, such as the barebox project (is this right?)
There is currently a migration from 8-bit micro-controllers to 32-bit micro-controllers in the deeply embedded space. These types of processors are used in industrial automation, sensors, infrastructure, and more…
(someone should fill this part in…)