# Is there a symbol for the antidiagonal matrix that has 1 as every entry?

Is there a symbol for the antidiagonal matrix that has 1 as every entry? For example, in two dimensions \begin{equation} \left( \begin{array}{cc} 0 & 1 \\ 1 & 0 \end{array} \right) \end{equation}

• Why you need a symbol, it's just antidiagonal matrix. I don't know any symbols though, and apart from identity matrix , most of the matrix don't have symbols. Nov 14, 2015 at 11:32
• Just take $I$, the symbol for the identity matrix, and rotate it through a right angle. Nov 14, 2015 at 12:00
• There is a multitude of reasons: 1. To make my working more readable. 2. To make it easier to refer to. 3. For use in mnemonics. I see you also had trouble referring to it as it's just antidiagonal matrix'' is ambiguous and doesn't make sense grammatically. Nov 14, 2015 at 12:01
• @JosephDewdney The symbol is $J_n$. en.wikipedia.org/wiki/Exchange_matrix Nov 14, 2015 at 13:41
• @calculus Thank you. If you change your comment to an answer I'll be able to mark it as my accepted answer. Nov 14, 2015 at 17:39

A row reversed identity matrix ($I_n$) can be denoted as $$J_n=\left( \begin{array}{} 0 & 0 & \ldots & 0 & 0 & 1 \\ 0 & 0 & \ldots & 0 & 1 & 0 \\ 0 & 0 & \ldots & 1 & 0 & 0 \\ \vdots & \vdots & & \vdots & \vdots &\vdots \\ 0 & 1 & \ldots & 0 & 0 & 0 \\ 1 & 0 & \ldots & 0 & 0 & 0 \\ \end{array} \right)$$
$J_n$ is also used to notate an all-ones matrix (see comment). On the other hand the all-ones matrix is often notated as $\textbf 1_n$. To avoid any confusion you have to define notations.
• But I've seen $J$ used to denote the all-ones matrix. Nov 14, 2015 at 21:51
• After I browsed the Internet I have seen that $J_n$ is also used to notate all-ones matrix. So your objection is absolute right. Thanks for theat I use $\textbf 1_n$ to notate an all-ones matrix. Nov 15, 2015 at 1:57
• And $J$ is often used for Jordan blocks as well: in a work where the Jordan reduction is used, it would be advisable to chose another notation for the exchange matrix. Apr 10, 2017 at 11:57