4 Images, Kernels, and Subspaces
... Definition. The kernel of a function whose range is Rn consists of all the values in its domain at which the function assumes the value 0. If f : X → Rn is a function from X to Rn , then ker(f ) = {x ∈ X : f (x) = 0}. Notice that ker(f ) is a subset of X. Also, if T (x) = Ax is a linear transformati ...
... Definition. The kernel of a function whose range is Rn consists of all the values in its domain at which the function assumes the value 0. If f : X → Rn is a function from X to Rn , then ker(f ) = {x ∈ X : f (x) = 0}. Notice that ker(f ) is a subset of X. Also, if T (x) = Ax is a linear transformati ...
