The video explains vectors from basic coordinates to advanced operations, covering magnitude, unit vectors, scalar/vector operations, and the dot and cross products. It highlights how dot products measure parallelism, cross products measure perpendicularity, and both are essential in understanding vector relationships.
Cosine similarity measures how similar two pieces of text (or vectors) are by calculating the cosine of the angle between them, giving a score from 0 (completely different) to 1 (identical). It focuses on the direction of the vectors rather than their magnitude, making it useful for comparing documents regardless of length.
Word embeddings represent words as numeric vectors so that semantically similar words are close in vector space, enabling machine learning models to process language. They can be created using frequency-based methods like TF-IDF, prediction-based models like Word2Vec or GloVe, or modern transformer-based contextual embeddings that adjust meaning based on surrounding words.
A vector database stores unstructured data as high-dimensional vector embeddings that capture semantic meaning, enabling similarity search based on closeness in vector space. Created via embedding models, these vectors can be efficiently queried using indexing methods like ANN, and are core to RAG systems for retrieving relevant context for LLMs.