I need to provide charts and transition maps on Grassmanian $(2,5)$. (All $2$-dimensional subspaces in $5$-dimensional space). I know how the charts look, used definition from this document: http://people.math.umass.edu/~tevelev/5-20.pdf
Now I have to write explicit transition functions (well, at least for one pair of charts). As far as I understand, I don't know exact form of those $A_{ij}$ matrices, so I am unable to write something like $A_{i^{\prime}j^{\prime}}^{-1}A$.
Why not take an order preserving transform. For example:
$$\begin{bmatrix}a&1&c&e&0\\b&0&d&f&1\end{bmatrix}\rightarrow \begin{bmatrix}1&a&0&c&e\\0&b&1&d&f\end{bmatrix} \ ?$$