Sorry if this question is a dumb one.


I used a special family of matroids in my research. One of them, of rank 3, can be represented by the following matrix over $\mathbb F\_5$ or over $\mathbb R$:


$\left(\begin{array}{cccccccccccc}
1&0&0&1 &1 &0 &-1&2 &-1& 2&0 &0\\ 
0&1&0&-1&0 &1 &2 &-1&0 & 0&-1&2\\
0&0&1&0 &-1&-1&0 &0 &2 &-1&2 &-1 \end{array}\right) $


It contains 12 points, 3 lines of 5 points, 7 lines of 3 points, all the other lines are of 2 points. It is a restriction of the Dowling geometry $Q\_3(\mathbb F\_5^\times)$. 


The other matroids of this type are represented over $\mathbb R$ by the matrix, the columns of which are all possible column vectors of length $n$ (the parameter) which contain either one nonzero entry (equal to $1$) or two such entries (equal to $1$ and $-1$, or $2$ and $-1$).


I would like to ask: is this class of matroids known? Any reference is welcome.


Here is a [geometric representation](https://i.stack.imgur.com/vJmAy.png) of the matroid above. The picture should be seen as a figure in projective plane, the dashed circle corresponding to the line at infinity.


Thanks!



Does this matroid have a name?
Matrices that contain at most two non-zero entries per column are called *frame matrices*. The matroids representable by frame matrices (over a finite field $\mathbb{F}$) are in fact a fundamental class in the structure theorem of Geelen, Gerards and Whittle for the class of all $\mathbb{F}$-representable matroids. I think the term *frame matroids* is being floated around as a possible name (at least this is what Geelen called them during a talk this week). This sort of conflicts with some earlier naming conventions though. For more information, check out the [Matroid Union Blog](http://matroidunion.org/?p=266). 


