# All elements of a matrix as a set

Suppose you have a matrix $A$. Is there a "standard"/mathematical elegant way to denote all members of the matrix as a set?

So suppose there is a matrix $A = \left[ \begin{array}{cc} a & b \\ c & d \end{array} \right]$ then I would like to define $set(A) = \{ a,b,c,d \}$

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If you define your own notation and it becomes popular, everybody will speak about the dtech-notation for matrix-elements! ;p – Raskolnikov Mar 29 '11 at 15:48
We call them the "entries of $A$", and usually refer to them that way. So you would write $\{x\mid x\text{ is an entry of }A\}$. – Arturo Magidin Mar 29 '11 at 15:49
$\cup_{ij}\{A_{ij}\}$, maybe. – mjqxxxx Mar 29 '11 at 15:58
There are some problems with this notation: in fact, something like $\{ a,b,c,d\}$ does not have "memory" of the place of each entry in the matrix (hence $A=\begin{pmatrix} a & b\\ c & d\end{pmatrix}$ and $B=\begin{pmatrix} a & c\\ d & b\end{pmatrix}$ have $set(A)=set(B)$ even if $A\neq B$), nor of the quantity of each entry in the matrix (therefore $I=\begin{pmatrix} 1 & 0\\ 0 & 1\end{pmatrix}$ and $M=\begin{pmatrix} 1 & 1\\ 1 & 0\end{pmatrix}$ have $set (I)= set (M)$ even if $I\neq M$)... – Pacciu Mar 29 '11 at 16:09
@Arturo Ok, $set(A)=\{x\;|\;x\,is\,an\,entry\,of\,A\}$ seem nice enough @Pacciu That is not a problem, that is just a consequence of transforming the matrix to a set. Clearly $set^{inv}$ can't exist and $set(A)$ might equal $set(B)$ even if $A \neq B$ but neither is required. – dtech Mar 29 '11 at 16:18