Recommend some good books to study vector space .
Thats the business of linear algebra, so books like Linear Algebra by Friedgerg & Insel et al. If you are done linear algebra, move on to an abstract algebra treatment by someone like dummit and foote.
I am studying them at the moment in my linear algebra course, im not sure how much detail you would like but the book we are using at the moment is quite good.
Anton Rorres, Elementary Linear Algebra with Applications (using ninth edn but doesnt matter)
At least give it a look, as i said, i find it quite useful.
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