In both Wikipedia and this medium post, I see the succinct principle components decomposition of X represented as
$$T=XW$$
However, it seems to me that it should be $T = WX$ instead, if according to the Wikipedia page that columns of $W$ are the eigenvectors of $X^TX$ and $X$ is arranged as row vectors for each observation. In short, $X \in \mathbb{R}^{nxk}$, where $n$ is the number of observations and $k$ is the dimension of each data point, and $W \in \mathbb{R}^{nxn}$, so $XW$ does not even exist.
Am I getting the derivation somewhere wrong?