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I came across the term free vector space in a book on mathematical physics by Geroch but cannot find them in any other of my books. Can someone give me an explanation of how a free vector space differs from a standard vector space. Geroch says that any set can be made into a free vector space but is this not true for a standard vector space by considering the set members as vectors and defining appropriate vector addition and scalar multiplication laws and a zero vector ?

Thanks Matheinste

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# Free vector space

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