What is the mathematical symbol of a space spanned by a matrix?

Question

Let's assume we have an $m\times n$ matrix $A$ and a vector $x\in R^n$. What is the mathematical symbol that points out to the space spanned by all vectors of $Ax$?

Is there any specific symbol for space vectors spanned by matrices?

Answer 1

Since your vector space is $\mathbb{R}^n$, you should be able to write $A\mathbb{R}^n$ (as trying noted), in analogy with $aS:=\{ax|x\in S\}$ for scaling a set of numbers.

Answer 2

This is the column space of $A,$ and a common notation is $CS(A)$ or $col(A)$.

Edit: Of course, $im(A)$ would also work..