# 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 read about n-vectors in https://en.wikipedia.org/wiki/N-vector but could not grasp it completely. Someone, please explain.

Next, "the linear combination of vectors V", does this talk about axpy operations with vectors inside the set V?

Third,"the usual vector algebra" what is that?

Thank you

• 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