Given a matrix $A=\begin{pmatrix}a&b\\c&d\end{pmatrix}$,
its transpose, obviously, is $A^T=\begin{pmatrix}a&c\\b&d\end{pmatrix}$.
But is there a conventional way of notating the matrix
 $\begin{pmatrix}d&b\\c&a\end{pmatrix}$
in terms of $A$?
This generalizes in an obvious way to larger matrices.
Also, do you know of some instance where this has been useful, especially in a geometric application?


I realize this seems like a dumb question, but I'm working on something where this matrix operation has come up in a significant way. It would be nice to see if anyone has had something similar happen.


For now I've been using $A\_T$.



Is there a standard notation for off-diagonal transpose?
In <http://arxiv.org/abs/math/0701936> (Fuchsian equations of type DN, by Vasily Golyshev and Jan Stienstra) the transpose of the matrix $A$ with respect to the anti-diagonal is denoted by $A^\tau$. It relates to the ordinary transpose $A^T$
(or $A^t$ as used in the paper), as follows:
$$A^\tau=JA^TJ$$
where $J=(J\_{ij})\_{0\le i,j\le n}$ denotes the matrix with $J\_{ij}=1$ if $i+j=n$
and $J\_{ij}=0$ otherwise. This fact was already noted by Pietro Majer for the case $n=1$ with notation $P$ instead of $J$ used in the Golyshev and Stienstra paper.


