T:V ->V is isomorphism, dim V = n. The kernel of isomorphism has only vector 0 in it, so by rank nullity theorem does it mean that dim of kernel is 1 and dim of image is n-1?
the question seems a little silly but I wasn't sure. thanks
2026-03-30 02:06:44.1774836404
dimension of kernel and image of isomorphism
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You mentioned right, that the kernel consists of only one point. But a space consisting of one point has dimension 0! This should answer your question. Maybe think about what a 1-dimensional space looks like.