This document presents a concise, math-forward background to vectorizing text into vectors (embeddings), explains why cosine similarity is a principled measure of semantic relatedness, and adds a dedicated section on “The math behind the Sentence-BERT algorithm.” The goal is to connect linear-algebraic derivations (e.g., PMI factorization) with modern transformer-based encoders used in practical SEO workflows. It also gives a brief overview of practical impact on modern SEO work like Topical authority, content clustering, internal linking and optimizing relevance for backlinks. In the end we also have a short introduction to IncRevs own Semantic Tool called "QueryMatch". This tool will be presented in its own research papers and case studies.