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Consider a vector $\pmb{v}=(v_1, v_2...,v_n) \in \mathbb{R}^n$ and a function $f: \mathbb{R} \to \mathbb{R} $. What is the best way to denote the vector $(f(v_1), f(v_2)....,f(v_n))$?

Writing $f(\pmb{v})$ isn't exactly correct as $f$ is not $\mathbb{R}^n \to \mathbb{R}^n$.

Edit: Based on comment below - imagine dimension of $\pmb{v}$ here is not known ahead of time.

EdOverflow
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ste_kwr
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    You could define $g:\Bbb R^n\to\Bbb R^n\ \text{via}\ g((v_1,v_2,...,v_n))=(f(v_1),f(v_2),...,f(v_n))$ and write $g(\mathbf v)$ for future usage? – Shubham Johri Jan 07 '19 at 18:57
  • Issue is that the length of vector $\pmb{v}$ is not known ahead of time. I can certainly get around writing the longform vector repeatedly by just redefining things, but would be good to know a proper way of denoting this stuff. It is not uncommon. – ste_kwr Jan 07 '19 at 19:16
  • Is that an issue? Just change the domain and codomain of $g$ to the set of tuples. – Shubham Johri Jan 07 '19 at 19:23
  • Agreed, no. But was hoping to see if there was a simpler, somewhat standardized way to do this. – ste_kwr Jan 08 '19 at 19:00

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You can handle this many ways. There is no consistent notation for this. Books and many programming lanuages handle it differently.

You pointed with $f(v)$ already a nice way out. It is just important to be clear on the notation, that means if it is not 100% obvious in the context define it that way.

Timmathy
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