Flipping a matrix?

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Real quick question:

I was wondering, how would one denote mathemathically the flipping of a matrix, horizontally or vertically, around its own axis?

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It seems there is a general agreement that no such notation already exists. As I suggested in a comment you could use $A^H$ and $A^V$. If I was writing in a document in French, I would use ${}^h\!A$ and ${}^v\!A$.

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Let $P$ be the matrix with $1$ on the antidiagonal and $0$ otherwise, that is $$P=\begin{pmatrix}0&0&\ldots& 0& 1\\0&0&\ldots & 1 & 0\\\vdots&\vdots &{}_.\cdot{}^\cdot&\vdots&\vdots\\ 0&1&\ldots& 0& 0\\1&0&\ldots& 0& 0\\ \end{pmatrix}.$$ Then $AP$ and $PA$ (and $PAP$) are flipped versions of $A$.