- #1
Master J
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The general linear group of a vector space GL(V) is the group who's set is the set of all linear maps from V to V that are invertible (automorphisms).
My question is, why is this a group? Surely the zero operator that sends all vectors in V to the zero vector is not invertible? But isn't it part of the definition of a group that an inverse exists for all elements?
My book tells me that it is not a vector space because of the above, but I can't see how it is even a group!
Can someone clear this up?
Thanks.
My question is, why is this a group? Surely the zero operator that sends all vectors in V to the zero vector is not invertible? But isn't it part of the definition of a group that an inverse exists for all elements?
My book tells me that it is not a vector space because of the above, but I can't see how it is even a group!
Can someone clear this up?
Thanks.