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}
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$\begingroup$ 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. $\endgroup$– Kushal BhuyanNov 14, 2015 at 11:32
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1$\begingroup$ Just take $I$, the symbol for the identity matrix, and rotate it through a right angle. $\endgroup$– Gerry MyersonNov 14, 2015 at 12:00
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$\begingroup$ 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. $\endgroup$– Joseph DewdneyNov 14, 2015 at 12:01
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1$\begingroup$ @JosephDewdney The symbol is $J_n$. en.wikipedia.org/wiki/Exchange_matrix $\endgroup$– callculus42Nov 14, 2015 at 13:41
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$\begingroup$ @calculus Thank you. If you change your comment to an answer I'll be able to mark it as my accepted answer. $\endgroup$– Joseph DewdneyNov 14, 2015 at 17:39
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1 Answer
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A row reversed identity matrix ($I_n$) can be denoted as $$J_n=\left( \begin{array}{} 0 & 0 & \ldots & 0 & 0 & 1 \\ 0 & 0 & \ldots & 0 & 1 & 0 \\ 0 & 0 & \ldots & 1 & 0 & 0 \\ \vdots & \vdots & & \vdots & \vdots &\vdots \\ 0 & 1 & \ldots & 0 & 0 & 0 \\ 1 & 0 & \ldots & 0 & 0 & 0 \\ \end{array} \right)$$
See here for further infomation.
$J_n$ 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.
answered Nov 14, 2015 at 18:17
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$\begingroup$ But I've seen $J$ used to denote the all-ones matrix. $\endgroup$ Nov 14, 2015 at 21:51
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$\begingroup$ 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. $\endgroup$ Nov 15, 2015 at 1:57
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$\begingroup$ 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. $\endgroup$ Apr 10, 2017 at 11:57