With a matrix $X_{n\times p}$ ($n>p$), we perform a principal component analysis:
$T_{n\times p}=X_{n\times p}W_{p\times p}$
where $W$ is the loadings matrix while $T$ is the scores matrix for $X$. Now, we can also perform a PCA for the transpose matrix of $X_{n\times p}$:
$\tilde{T}=X^T \tilde{W}$
where $\tilde{W}$ is the loadings matrix while $\tilde{T}$ is the scores matrix for $X^T$. What is the relationship between $T$ and $\tilde{W}$? And what is the relationship between $W$ and $\tilde{T}$?