kärnform
Kärnform, in Swedish mathematical terminology, refers to what is commonly called the kernel of a function or linear transformation. The kernel consists of all inputs that map to the zero element of the codomain.
For a linear map T: V → W, the kernel is ker(T) = {v in V | T(v) = 0}.
To determine the kernel of a matrix A, one solves the homogeneous system Ax = 0. Row-reduction yields
Example: Let A be the 2×3 matrix [[1, 0, 0], [0, 1, 0]]. Solving Ax = 0 gives
Context and usage: The kernel or kärnform is central in solving linear systems, understanding linear relations
Etymology and usage: Kärnform is the Swedish term for kernel; in English-language texts the word kernel is