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in information retrieval Vector embeddings represent documents and queries in a numerical vector format that means that we can take some texts which could be web pages from the internet in the case of Google or maybe product descriptions in the case of Amazon and we can encode it using some sort of embedding method or model and we all get something that looks like this so we have now represented our text in a vector space now there are different ways of doing this and sparse and dense vectors are two different forms of this representation each with their own pros and their own cons typically when we think of sparse vectors things like TF IDF and bm25 they have very high dimensionality and they contain very few non-zero values so the information within those vectors is very very sparsely located and with these types of vectors we have Decades of research looking at how they can be used and how they can be represented using compact data structures and there are naturally many very very
