# What is the standard notation for reversing the order of vector's components? [closed]

If we have a vector $x=(x_1,x_2,\ldots,x_n)$, is there any standard way to denote the vector $(x_n,x_{n-1},\ldots,x_1)$?.

I think that $x^{-1}$ could be a good option.

• For a permutation of indices $\sigma$, I would denote $x_\sigma:=(x_{\sigma_1},\dots x_{\sigma_n})$, (or $x\sigma$ or $x\circ\sigma$ or $x^\sigma$). Dec 9 '16 at 11:26
• @PietroMajer: And how do you denote the permutation $\sigma(i)=n+1-i$ of $\{1,\dotsc,n\}$? Dec 9 '16 at 11:46
• My 2c: how about $x^\leftarrow$? Dec 9 '16 at 11:53
• @ HeinrichD, yes, this is the question Dec 9 '16 at 12:04
• Instead of $x$, name your vector $b$ and the reversed one $d$. Dec 9 '16 at 12:33

An alternative would be to define and use the exchange matrix (see the Wikipedia entry “Exchange matrix”) $$J = \begin{pmatrix} 0 & 0 &\cdots &0 & 1\\ 0 & 0 & \cdots & 1 & 0\\ \vdots & \vdots &\ddots & 0 & 0\\ 0 & 1 &\cdots & 0 &0\\ 1 & 0 &\cdots & 0 &0 \end{pmatrix}$$ and to note that $(x_n, \dotsc, x_1)=J (x_1, \dotsc, x_n)$.
I think that $\mathrm{flip}(x)$ is a better choice. This is also used in some programming languages. Notice that $x^{-1}$ could be easily confused with $(x_1^{-1},\dotsc,x_n^{-1})$.