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freeCodeCamp

Linear Algebra for Machine Learning

via freeCodeCamp

Overview

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This comprehensive 10-hour course explores all critical linear algebra concepts essential for machine learning, providing the mathematical foundations needed to excel in AI. Master fundamental topics including trigonometry, geometry, vector spaces, norms, Cartesian coordinate systems, and vector operations. Progress through increasingly advanced concepts such as scalar multiplication, linear combinations, spans, linear independence, matrices, determinants, vector projections, orthogonality, and special matrix properties. Learn practical applications of vectors in real-world scenarios like word count analysis and customer purchase representation. Created by LunarTech_ai, the course methodically builds from basic principles to complex mathematical concepts, ensuring a solid foundation for applying linear algebra in machine learning contexts.

Syllabus

00:00:00 - Introduction
00:02:09 - Essential Trigonometry and Geometry Concepts
00:10:52 - Real Numbers and Vector Spaces
00:15:05 - Norms, Refreshment from Trigonometry
00:19:52 - The Cartesian Coordinates System
00:24:37 - Angles and Their Measurement
00:38:00 - Norm of a Vector
00:44:08 - The Pythagorean Theorem
00:52:00 - Norm of a Vector
00:56:00 - Euclidean Distance Between Two Points
01:11:33 - Foundations of Vectors
01:12:50 - Scalars and Vectors, Definitions
01:42:28 - Zero Vectors and Unit Vectors
01:49:39 - Sparsity in Vectors
01:52:39 - Vectors in High Dimensions
01:55:14 - Applications of Vectors, Word Count Vectors
02:03:22 - Applications of Vectors, Representing Customer Purchases
02:39:22 - Advanced Vectors Concepts and Operations
02:40:40 - Scalar Multiplication Definition and Examples
03:04:27 - Linear Combinations and Unit Vectors
03:51:37 - Span of Vectors
04:31:42 - Linear Independence
05:03:34 - Linear Systems and Matrices, Coefficient Labeling
05:20:24 - Matrices, Definitions, Notations
05:50:24 - Special Types of Matrices, Zero Matrix
06:25:25 - Algebraic Laws for Matrices
07:21:56 - Determinant Definition and Operations
08:12:47 - Vector Spaces, Projections
08:20:05 - Vector Spaces Example, Practical Application
09:14:33 - Vector Projection Example
09:29:35 - Understanding Orthogonality and Normalization
10:06:29 - Special Matrices and Their Properties
10:21:07 - Orthogonal Matrix Examples

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freeCodeCamp.org

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