Let $M$ be a matroid and $x$ is a loop in it, which means $x$ is not in any independent set of $M$. Then $M$ is also a simplicial complex (all its independent sets are faces).
Then I feel confused to find the connectivity $\eta(M)$. Is it same as $\eta(M-\{v\})$, where $\eta(X)$ for a simplicial complex $X$ is the largest $k$ that for any $i\le k$ and simplicial map $f:T(S^i)\to X$, $f$ can be extended to $\bar{f}:T(B^{i+1})\to X$, plus 2. ($T(X)$ means triangulation of $X$.)
As in the definition of simplicial map, typically it is from and to the union of faces of a simplicial complex. If $x$ is not in any face, how do we deal with $x$?