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I am not very experienced in this field, so, I have a rather simple question

-Consider a linear vector space V of dimension 4.

-Prescribe that, if two vectors in V differ by a nonvanishing constant, they belong to the same equivalence class.

-Put together all these equivalence classes, and obtain a 3-dimensional vector space P(V).

My question is: is the space P(V) obtained as outlined above the "projective space" one encounters in projective geometry -- the one defined using axioms, see e.g. the book by Coxeter.

Additional question: if the initial vector space V is defined over the field of real numbers, is P(V) the same as the "real projective space" (obtained from ℝ^4\{0} by projection)?

Any help is very much appreciated,

Ivl

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# From a vector space to the projective space

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