Definition: Kernel
Let and be vector spaces.
The kernel of a linear transformation is the set of all vectors which the transformation sends to the zero vector in :
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Definition: Kernel
Let (V,F,+,⋅) and (W,F,+,⋅) be vector spaces.
The kernel of a linear transformation T:V→W is the set of all vectors v∈V which the transformation sends to the zero vector in W:
ker(L)=def{v∈V∣T(v)=0W}