Null Space of a Linear Transformation

Let U and V be two vector spaces over the same field F and let T be a linear transformation from U into V.

The null space of T is the set of all those vector α in U such that T(α)=0 (since zero vector of V

The null space of T is written as N(T) thus

N(T)={α∊U:T(α)=0}

Thus null space of a linear transformation of T is also called Kernel of T.