In this thread, the convergence of coefficient for univariate dependent variable is proven. I wonder, assuming the same setup, how can the convergence be extended to multivariate as: $$Y=XW+\epsilon$$ where $Y_{n\times d}$, $X_{n\times d}$, $\epsilon_{n\times d}$ and $W_{d\times d}$.
My issue is how to write the $X'Y$ part of $\hat{W}=(X'X)^{-1}X'Y$ using $x_i$ and $y_i$ which are the column vector ($d\times 1$) of observation $i$ (each row of matrix $X$ and $Y$ respectively). When we write this term in this format, can we say based on WLLN as $n\rightarrow\infty$ the term converges to $E[X'Y]$?