Proteins, large molecules composed of many amino acids, are required for the function and regulation of the body's cells, tissues, and organs. The conformational characteristics of proteins, such as entanglement, are related to their function. Simplifying the representation of these macromolecules, they can be imagined as mathematically simple (closed or open) curves in space. This representation allows the use of knot theory to study their entanglement complexity. A simple measure of entanglement between two open or closed curves is the Gauss linking integral. In this study, the Gauss linking integral is employed to quantify the local and global entanglement in the protein backbone. More precisely, the linking integral between different portions of the chains is estimated. In analogy to the knotting fingerprint, we define the linking matrix fingerprint of proteins. This is a matrix representation of the molecule that encodes the linking of all its sub-chains. Using data compression, the most important topological features of a given conformation are extracted and analyzed. The development and testing of this new method to analyze the spatial structure of proteins provides a better understanding of their function. Furthermore, it may be used to devise methods to control their function and, as a consequence, treat or prevent diseases.