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In this answer I am using a transformation of matrices, and I would like to know if there is a notation for this.

Given a matrix $A$, let $B$ be the same as $A$ with rows in reverse order, $C$ with the columns in reverse order, and $D$ with both rows and columns in reverse order. Is there a usual notation for any of $B,C$ or $D$ ?

The $D$ case has a nice property: if it's called $f$, then for any matrices $A,B$, $f(AB)=f(A)f(B)$.

I know one can write for instance $B=A[n:1,:]$ and it's not uncommon to see such MATLAB-like formulas in numerical analysis articles, but I wonder if there is a shorthand for this, or a usual name.

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I don't know of anything like that in standard mathematical usage, but the APL programming language has operators $C = ⌽A$ and $B = \ominus A$.

Then your theorem is that $$⌽\ominus(XY) = (⌽\ominus X)(⌽\ominus Y)$$ or more briefly that $⌽\ominus$ is a homomorphism. (Clearly, $⌽\ominus = \ominus⌽$.)

Probably nobody would complain much if you used something like that.

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  • $\begingroup$ I didn't think of APL. Interesting notation. Following your suggestion, I found a list of APL symbols here. $\endgroup$ – Jean-Claude Arbaut May 21 at 4:57

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