To build systems capable of understanding meaning, we first need a way to represent data like text or images numerically. This chapter focuses on vector embeddings, which serve as this numerical representation, placing data points within a high-dimensional vector space.

We will start with a review of how different types of data are converted into vectors. You will learn about common embedding models, particularly those based on transformer architectures, and discuss the impact of vector dimensionality on system performance. We will also introduce techniques for dimensionality reduction. A key aspect of working with vectors is measuring how similar they are; therefore, we will compare metrics such as Cosine Similarity ($cos(\theta)$), Euclidean Distance ($||\vec{a} - \vec{b}||_2$), and the Dot Product ($\vec{a} \cdot \vec{b}$). Finally, you'll apply these concepts by generating embeddings using Python libraries and calculating their similarity.