To show the orbit of $x$ under the action of some matrix $H$ we can write:
$$ x \xrightarrow{H} Hx \xrightarrow{H} H^2x \xrightarrow{H} \cdots $$
where the '$\text{ }\xrightarrow{H}\text{ }$' symbol communicates left-multiplication by $H$.
What symbology do we have to show the orbit of an object under right-multiplcation?
e.g. given $F$ and compatible object $z$, do we have arrow symbology for
$$z \to zF \to zF^2 \to \cdots $$
If $x$ is a column vector, the matrix $H$ operates on it from the left. If $z$ is a row vector, the matrix $F$ operates on it from the right. Usually, there is only one conventual way to have a matrix act on a vector. I don't think there are enough ambiguous contexts for there to be a conventional disambiguation.
Which is to say, if you need such a notation, either invent one that seems reasonable and use a couple of words to describe it the first time it's being used. Or use a couple of words next to wherever such a chain is written down to specify the direction.