Abstract Any conformational ensemble of biopolymers, whether they are proteins or chromosomes, can be described using contact matrices derived from experimental or computational studies. One powerful approach to extract meaningful information from these contact matrices is to perform principal component analysis (PCA) on the covariance matrix of the contact data. Indeed, PCA on Hi-C chromosome contact matrices has revealed the spatial segregation of active and inactive chromatin. Separately, PCA on contact matrices from snapshots of protein conformations has characterized correlated fluctuations of protein domains. However, despite the similarities of these data and analyses, there has been little synergy between the PCA approaches and the comparison of resulting biological insights obtained for protein and chromosome structures. We note that, to date, different styles of analyses were applied exclusively to each biomolecule type: explicit contact correlation analysis (E-PCA) for proteins and implicit contact correlation (I-PCA) for chromosomes. In this work, we compare the results of applying both methods to both classes of biopolymers. While I-PCA reveals only average features of 3D chromosome structure, we find that applying E-PCA to an ensemble of chromosome structures from microscopy data reveals the dominant motion (concerted fluctuation) of the chromosome. Applying E-PCA to Hi-C data across the human blood cell lineage isolates the aspects of chromosome structure that most strongly differentiate cell types. Conversely, when we apply I-PCA to simulation snapshots of two protein complexes, the major component reports the consensus features of the structure, while the previously applied E-PCA characterizes correlated deviations from the mean structure.