Linear Algebra for Machine Learning and Generative AI

Embark on a comprehensive 6-hour linear algebra course designed for beginners, focusing on essential skills for data science, machine learning, and AI applications. Explore a wide range of topics, from vector foundations and operations to matrix concepts and solving linear systems. Gain practical knowledge through real-world examples and geometric representations. Begin with an introduction to the course and a roadmap for mastering linear algebra in 2024. Refresh your understanding of real numbers, vector spaces, norms, and Euclidean distance before diving into vector concepts, special vectors, and their applications. Progress to advanced vector operations, dot products, and the Cauchy-Schwarz inequality. Conclude with an in-depth look at linear systems, matrices, and Gaussian elimination techniques. Benefit from detailed examples and step-by-step explanations throughout the course, ensuring a solid foundation in linear algebra for your future endeavors in mathematics and artificial intelligence.

⌨️ Introduction to the course
⌨️ Linear Algebra Roadmap for 2024
⌨️ Course Prerequisites
⌨️ Refreshment: Real Numbers and Vector Spaces
⌨️ Refreshment: Norms and Euclidean Distance
⌨️ Why These Prerequisites Matter
⌨️ Foundations of Vectors
⌨️ Vector - Geometric Representation Example
⌨️ Special Vectors
⌨️ Application of Vectors
⌨️ Vectors Operations and Properties
⌨️ Advanced Vectors and Concepts
⌨️ Length of a Vector - def and example
⌨️ Length of Vector - Geometric Intuition
⌨️ Dot Product
⌨️ Dot Product, Length of Vector and Cosine Rule
⌨️ Cauchy Schwarz Inequality - Derivation & Proof
⌨️ Introduction to Linear Systems
⌨️ Introduction to Matrices
⌨️ Core Matrix Operations
⌨️ Solving Linear Systems - Gaussian Elimination
⌨️ Detailed Example - Solving Linear Systems
⌨️ Detailed Example - Reduced Row Echelon Form Augmented Matrix,REF, RREF