Vectors are mathematical representations of data in a format that AI algorithms can understand. They consist of an ordered series of numbers and have a dimensionality, which is the number of numbers in the vector. Vectors are used to represent meaningful information in a way that's associated with a domain object, such as a business object or text. The process of converting this information into a vector is called embedding. Vector databases store and retrieve data in a way that's all about context, using algorithms like squared Euclidean distance and cosine similarity to compare vectors. These similarities are used to find the closest vector to a query vector, which is referred to as a "vector search" or "similarity search." This approach is useful in AI systems for tasks such as natural language processing, generative AI, and retrieval augmented generation (RAG). Vectors and vector databases are essential components of many AI systems, providing relevant contextual information that can be used to prevent LLM hallucinations and enable responses based on the latest data.