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).(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# General Linear Group of a Vector Space

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