Let $P(M,G)$ be a principal $G$ bundle. Let $\omega$ be a connection $1$ form on $P(M,G)$. This is a $\mathfrak{g}$ valued $1$ form on $P$ i.e., for each $p\in P$, we have $\omega(p):T_pP\rightarrow \mathfrak{g}$.
This Wikipedia page says we can think of $\omega$ as a matrix of $1$-forms (I believe they mean the usual real valued $1$ forms). I do not understand what they mean here.
I think they are assuming $\mathfrak{g}$ is sub algebra of $M(n,\mathbb{R})$ for some $n$.
Then, given $p\in P$, we have $\omega(p):T_pP\rightarrow \mathfrak{g}$. So, for $v\in V$, $\omega(p)(v)$ is a real valued $n\times n $ matrix.
Suppose $\omega(p)(v)=[a_{ij}]_{1\leq i,j\leq n}$. If we vary $v$ along $T_pP$, what we get are functions $a_{ij}:T_pP\rightarrow \mathbb{R}$.
With this, we have $\omega(p)(v)=[a_{ij}(v)]_{1\leq i,j\leq n}$, here $a_{ij}$ are maps $T_pP\rightarrow \mathbb{R}$.
Ignoring $v$, we see that $\omega(p)=[a_{ij}]_{1\leq i,j\leq n}$ where $a_{ij}:T_pP\rightarrow \mathbb{R}$.
So, once we fix $p\in P$, we have $a_{ij}:T_pP\rightarrow \mathbb{R}$. To show dependence on $p$, we write $a_{ij}(p):T_pP\rightarrow \mathbb{R}$.
So, for each $p\in P$, we have $a_{ij}(p):T_pP\rightarrow \mathbb{R}$. This is what a $\mathbb{R}$ valued $1$ form on $P$ comes with. For each $p\in P$, it comes with a map $T_pP\rightarrow \mathbb{R}$.
See $a_{ij}$ as a $1$ form on $\mathbb{R}$ as for each $p\in P$ we have $a_{ij}(p):T_pP\rightarrow \mathbb{R}$. So, we have $n^2$ real valued $1$ forms on $P$. We can denote this by $\omega=[a_{ij}]$ or in a more better way $\omega=[\omega_{ij}]$ (replaced the notation $a_{ij}$ with $\omega_{ij}$).
Is this the matrix of $1$-forms they are talking about?
If this is true, same is the case with curvature form. Given $p\in P$ we have $\Omega(p):T_pP\times T_pP\rightarrow \mathfrak{g}$. Again, for each pair $(v_1,v_2)$ we have a matrix $\Omega(p)(v_1,v_2)=[a_{ij}]$.
Same thing as above, we can write $\Omega=[\Omega_{ij}]$ where $\Omega_{ij}:P\rightarrow \Lambda^2 TP$ given by $\Omega_{ij}(p):T_pP\times T_pP\rightarrow \mathbb{R}$, $\Omega(ij)(p)(v_1,v_2)$ is a $i,j$ element in in the matrix $\Omega(p)(v_1,v_2)$ (being an element of $\mathfrak{g}$).
Is this what it mean to say a connection form is given by matrix of $1$-forms?