My question: What is a notation for an empty 0x0 matrix (i.e. the matrix for the only linear map $f:\{0\}\to\{0\}$)? Is it written $()$? How can I distinguish the 0x0 matrix with for example the 0x3 matrix or the 3x0 matrix?
What I have already found out: Concerning the section “Empty matrices” of the Wikipedia article “Matrix (mathematics)” there “is no common notation for empty matrices”. But unfortunately I haven't found any notation so far...
Notes: I am looking for a notation which is used in a textbook. I am not interested in how empty matrices can be created in CAS like Matlab, Mathematica, etc.
Reason for this question: In our course we had the task to draw all graphs with three vertices and to state the incidence matrix for each drawn graph. Thus, for the empty graph I have to state a 0x3 matrix, but I didn't know the right notation for it...
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$\begingroup$I don't think there is any universally recognizable notation for this. Whatever choice one might make, without explanation it could easily be misunderstood, is the point.
(For that matter, I can't help wondering how/why the notation would be needed in a context that wouldn't permit the simpler explanation "unique linear map from $k^0$ to $k^0$".)
$\endgroup$ $\begingroup$I think the most simple notation would be to write $$ 0_{M_{0,0}}$$ for a matrix of size $0\times 0$, and $$ 0_{M_{3,0}}$$ for a matrix of size $3\times 0$.
It's very similar when you want to write the zero of an unknown field $F$, when you write $0_F$.
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