# Vector Space definition in Springer Text

The definition of vector space goes like this. Let V be a set of n-vectors such that any linear combination of the vectors in V is also in V. Such a set together with the usual vector algebra is called a vector space.

• I’m pretty sure that’s not what’s meant by an “n-vector” in the Springer text. It’s probably just a synonym for $n$-tuple. – amd Feb 1 '18 at 7:41
• I agree with @amd . The Wikipedia page defines an $n$-vector as a normal vector over a surface. The statement "Let V be a set of n-vectors such that any linear combination of the vectors in V is also in V. Such a set together with the usual vector algebra is called a vector space." is informally talking about the vector space $\Bbb R^n$, supposing the reader is familiar with it. – Crostul Feb 1 '18 at 7:44