# Is there any shorthand for $\text{span}\{v_1, \ldots,v_n\}$ which doesn't conflict with any notation in linear algebra?

Some people use $\langle \cdot \rangle$ as a shorthand of $\text{span}$ (e.g. the German wiki), i.e.

$$\langle \{ v_1, \ldots,v_n \} \rangle := \text{span}\{v_1, \ldots,v_n\},$$

yet the notation seems to be suboptimal due to its similarity with the inner product.

Is there any handy notation for $\text{span}\{v_1, \ldots,v_n\}$ which doesn't conflict with any another notation in linear algebra?

Here is what I've tried: $[v_1, \ldots,v_n]$ seems to be simple and vacant.

• $\operatorname{span}$ is already pretty short. Why do you need an even "shorter" hand? – user137731 Dec 4 '14 at 21:14
• There is no syntactic ambiguoty between inner product $\langle v,w\rangle$ and span $\langle \{v,w\}\rangle$ (or $\langle S\rangle$). The notation with $\langle\;\rangle$ is also common for groups generated by ..., though this is not called span. – Hagen von Eitzen Dec 4 '14 at 21:21
• It's also used for "ideal generated by" as well. So using it for "subspace generated by" is not too bad. – Nishant Jan 10 '15 at 4:40

If $V$ is a vector space over $k$ then you could denote the span of $v_1, \ldots, v_n \in V$ by $kv_1 + \ldots + kv_2$, i.e. as a sum of one-dimensional vector spaces. This notation looks nicer for particular fields such as $\mathbf{R}$ or $\mathbf{C}$: they look like $\mathbf{R}v_1 + \ldots + \mathbf{R}v_n$ and $\mathbf{C}v_1 + \ldots + \mathbf{C}v_1$ respectively.
If the elements $v_i$ are linearly independent then the sum is direct and you can write $\bigoplus kv_i$.
None that I know of. This is not really an answer but I have no reputation to comment... The $[v_1,...,v_n]$ is bad in particular when $n=2$ since it could be confused with a Lie bracket. (And for higher $n$ with higher Lie brackets.)
Edit: I sometimes use/see used $\mathbb{K}\{v_1,...,v_n\}$. But it doesn't save many letters.