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    This is probably trivial to answer, but why does ker(T)={0} imply that nullity(T)=0 for a general linear transformation T i.e why is the dimension of {0} zero and not one? How can you form the zero vector without any vectors to begin with?

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    (Original post by Implication)
    This is probably trivial to answer, but why does ker(T)={0} imply that nullity(T)=0 for a general linear transformation T i.e why is the dimension of {0} zero and not one? How can you form the zero vector without any vectors to begin with?

    Thanks.
    Because the empty set is a basis for \left\{0\right\}, this is partially by convention/definition. The span of a set of vectors is the intersection of all subspaces containing them, and so the span of no vectors is the intersection of all subspaces which is \left\{0\right\}.
 
 
 
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