Linear Algebra for AI: Foundations of Vector Geometry

Modern artificial intelligence and machine learning algorithms are built entirely on the language of mathematics. To truly understand how models process data, you must first grasp the core concepts of linear algebra and how they translate to computer algorithms. This text-based course guides you through the foundational mathematics of AI, helping you build a strong intuitive understanding of vector spaces and matrix operations. By working through clear written explanations and practical code examples, you will bridge the gap between abstract mathematical theory and real-world AI applications. You will learn how data is represented, transformed, and manipulated under the hood in modern machine learning workflows. What you'll learn: - Understand foundational concepts of vector geometry, vector spaces, and coordinate systems - Perform essential matrix operations including multiplication, transposition, and inversion - Apply linear transformations and visualize how they manipulate data spaces - Implement mathematical operations programmatically using modern Python libraries like NumPy - Explore how high-dimensional vector spaces form the basis of modern AI embeddings and neural networks We begin with the absolute basics, introducing key terminology, geometric intuition, and fundamental definitions before moving on to practical applications. You will progress from simple 2D vector coordinates to complex multidimensional transformations, learning how to write clean, vectorised Python code to solve algebraic problems. This course is designed specifically for beginners, aspiring data scientists, and software developers who want to understand the math behind AI. No advanced mathematical background is required to start. Begin your journey into the mathematical foundation of modern artificial intelligence today.