# Notation, Vector space

I have a question to the following notation, which I have not seen before:

Given are the vectors $x=\,^t(x_1,\dotso, x_n)\in\mathbb{Q}^n$.

Show that $(_\mathbb{Q}\mathbb{Q}^n,\oplus,\odot)$, with the vector addition and scalar multiplication from $(_\mathbb{R}\mathbb{R}^n,\oplus,\odot)$, is a vector space

My question is, what $_\mathbb{Q}\mathbb{Q}^n$ and $_\mathbb{R}\mathbb{R}^n$ is supposed to be?

My guess is, that it is simply meant, that $x_i\in\mathbb{Q}$ for $1\leq i\leq n$

But that is in my opinion just a pointless notation... Does someone of you know, what this means?

Thanks in advance.

[context: Someone asked me to help him with this question and he told me, that the holder of the lecture does not know it either... I dont know the lecture notes or visit the lecture either]

• An educated guess but the subscript might be to emphasise the scalar field of your vector space. For example, $\mathbb{C}$ is different when considered as a 2-d $\mathbb{R}$ vector space or a 1-d $\mathbb{C}$ vector space. – daruma May 29 '17 at 14:43

## 1 Answer

I think that $_\mathbb{Q}\mathbb{Q}^n$ means a vector space $\mathbb{Q}^n$ over the field $\mathbb{Q}$ and $_\mathbb{R}\mathbb{R}^n$ means a vector space $\mathbb{R}^n$ over the field $\mathbb{R}$