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# Linear Transformations - nullity Watch

1. 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.
2. (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 , 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 .

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