1
$\begingroup$

I am wondering if there is any notation for the following operation of a sort of concatenation of vectors. For example if I have a vector $x=(x_1,\dots,x_n)\subseteq\mathbb{F}^n$ and $y\in\mathbb{F}$ is there any notation for extending $x$ into $\mathbb{F}^{n+1}$ with the vector $(x_1,\dots,x_n,y)$? I have seen the notation $(x,y)$ given before, but these seems counter-intuitive to me I would read it as an $2$-tuple consisting of an $n$-tuple followed by a number from $\mathbb{F}$. Is there any better notation?

$\endgroup$
1
  • 1
    $\begingroup$ I would say identification of $ F^n\times F $ and $ F^{n+1} $ is as obvious as it gets. If you want to make sure, mention it before using it. $\endgroup$ – Bananach Dec 6 '17 at 22:29
1
$\begingroup$

You could do something like $(\mathbf{x},y)$ or $(\vec{x},y)$, however you usually denote a vector. I suppose $\mathbf{x} \oplus y \in\mathbb{F}^n \oplus \mathbb F $ is okay as well, but it's clunky and really ugly/ asymmetric.

For the sake of consistency (especially if there is no reason to distinguish elements in the $n+1$-tuple), I really think $(x_1, \dots,x_n,y)$ is best for clarity, and it doesn't strike me as too cumbersome.

$\endgroup$
1
$\begingroup$

Assuming I'm following your question,I prefer this notation $$\left(\vec{x}_n,y\right):= (x_1,x_2,\ldots,x_n,y)$$

That's a vector arrow above $x_n$, not very visible for some reason.

$\endgroup$
0
$\begingroup$

The standard mathematical notation for concatenation of tuples is $$ u || v $$ (see here). Thus $$ (x_1,\ldots,x_n) ||y = (x_1,\ldots,x_n, y) $$

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.