In my current data analysis problem I am using models with complicated penalty structure that is a result of operations on some matrix $Q$.
I do know definitions of basic matrix operations:
- $Q^T$
- $Q^{-1}$
- $QQ^T$
but I feel I lack intuitions / imagination what is going on with $Q$ when undergoes these operations.
Eventually, I would like to get the feeling what is done here:
- $Q_{res} = Q^T(QQ^T)^{-1}Q$
- $W_{res} = W (a(I-Q_{res}) + b Q_{res})^{-1}$
for some
- $Q: dim(Q)=[n_1,n_2]$, a subspace containing some structure relevant to variables (columns) of $W$,
- $W: dim(W)=[n_3, n_2]$, subjects' (rows) observations of some variables (columns) of which (variables) we have some knowledge of its structure.
I kindly ask for some explanation / good material references.