PCA can be construed as a loss compression of the data matrix. In fact, Eckart-Young theorem shows that this is an optimal compression (optimal w.r.t low rank,

PCA can be construed as a loss compression of the data matrix. In fact, Eckart-Young theorem shows that this is an optimal compression (optimal w.r.t low rank, i.e. space to hold the values). In the language of OP, this shows the minimal energy loss for a given space constraint. The key word is "lossy". It may as well be that the loss'ed part had the signal for further classification down the pipeline. Or may be not. It depends on the case.