Linear Algebra Foundations for AI and Large Language Models

Many developers want to transition into AI and large language model development, but find themselves blocked by the underlying mathematics. While application-level APIs are accessible, understanding how models actually process, transform, and learn from data requires a solid grasp of linear algebra. This text-based course bridges the gap between traditional programming logic and mathematical AI concepts. You will transition from thinking in loops and conditionals to thinking in vectors, matrices, and high-dimensional spaces, giving you the confidence to read AI research, work with modern vector databases, and understand how model weights operate. What you'll learn: - Learn foundational linear algebra terminology, including vectors, matrices, scalars, and tensors. - Understand matrix multiplication and its direct application to neural network layers and weight transformations. - Apply vector operations to modern AI concepts like embeddings, similarity metrics, and semantic search. - Explore how dot products power the attention mechanisms in transformer-based large language models. - Practice calculating vector distances to understand how vector databases retrieve relevant context. - Master coordinate spaces and geometric transformations to visualize high-dimensional data structures. The course begins with fundamental definitions and core mathematical concepts before progressing to practical AI applications. You will work through written explanations, clear formulas, and conceptual code snippets designed to make abstract math tangible. This course is designed for programmers, software engineers, and tech enthusiasts who want to build a career in AI but lack a formal background in advanced mathematics. No prior linear algebra experience is required. Start reading today to unlock the mathematical secrets behind modern artificial intelligence.