I'm working with Principal Component Analysis (PCA) on molecular data, specifically focusing on the Cartesian coordinates of atoms within molecules. My goal is to preprocess this data for a machine learning model, and as part of this process, I'm applying PCA to decorrelate and normalize the data. A crucial step involves removing the influence of global translation and rotation to focus on the intrinsic properties of the molecules.
According to ChatGPT, the first three principal components typically account for global translation along the x, y, and z axes, and the next three components are often associated with rotation around these axes. But the chatbot fails to provide any evidence to support this argument. I'm looking for a deeper understanding of why exactly these first six components correspond to global translation and rotation. How does PCA inherently capture these movements as the dominant sources of variance in the data?