In the era of dense retrieval, document indexing and retrieval is largely\nbased on encoding models that transform text documents into embeddings. The\nefficiency of retrieval is directly proportional to the number of documents and\nthe size of the embeddings. Recent studies have shown that it is possible to\nreduce embedding size without sacrificing - and in some cases improving - the\nretrieval effectiveness. However, the methods introduced by these studies are\nquery-dependent, so they can't be applied offline and require additional\ncomputations during query processing, thus negatively impacting the retrieval\nefficiency. In this paper, we present a novel static pruning method for\nreducing the dimensionality of embeddings using Principal Components Analysis.\nThis approach is query-independent and can be executed offline, leading to a\nsignificant boost in dense retrieval efficiency with a negligible impact on the\nsystem effectiveness. Our experiments show that our proposed method reduces the\ndimensionality of document representations by over 50% with up to a 5%\nreduction in NDCG@10, for different dense retrieval models.\n