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.
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Sign up to join this communityIf 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.
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 $(x_1^{-1},\dotsc,x_n^{-1})$.