Suppose V and V0 are ﬁnitely-generated vector spaces and T : V → V0 is a...

Suppose V and V0 are ﬁnitely-generated vector spaces and T : V → V0 is a linear transformation with ker(T) = {~ 0}. Is it possible that dim(V ) > dim(V0)? If so, provide a speciﬁc example showing this can occur. Otherwise, provide a general proof showing that we must have dim(V ) ≤ dim(V0).

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Colby Messinger answered 1 year ago

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