About this course

This course aims to deliver a comprehensive understanding of Linear Algebra, vital for students from diverse fields like economics, engineering, physics, and statistics. It is designed to enrich your mathematical toolkit with advanced algebra and geometric concepts, leading to better problem-solving abilities. Initially intended for first-year engineering students at EPFL, this MOOC is split into three parts and is equally beneficial as a standalone course for anyone passionate about mathematics.

Course Description

The course provides a detailed exploration of various linear algebra concepts through ten chapters, focusing on both theory and applications. It covers a broad spectrum of topics from solving linear equations to understanding orthogonal matrices and symmetric matrices.

What students will learn from the course

• Define and provide illustrative examples of theoretical concepts.
• Recognize inner products and understand properties like the Cauchy-Schwarz Inequality.
• Understand orthogonality concepts and construct orthonormal bases using the Gram-Schmidt process.
• Calculate the best quadratic approximation of a vector and understand least squares solutions for linear systems.
• Compute QR factorization of matrices, orthogonal diagonalization of symmetric matrices, and singular value decomposition.

Prerequisites

Students should have a high school diploma, a firm grasp of high school algebra, and a solid understanding of content from previous parts of this course, specifically Linear Algebra Part 1 and Part 2.

Course Outline

• Linear Systems
• Matrix Algebra
• Vector Spaces
• Bases and Dimensions
• Linear Transformations
• Matrices and Linear Transformations
• Determinants
• Eigenvalues, Eigenvectors, Diagonalization
• Inner Product Spaces and Euclidean Spaces
• Orthogonal and Symmetric Matrices

Who this course is for

• Students from fields such as Engineering, Physics, Economics, and Statistics
• Learners interested in advancing their mathematical knowledge
• Anyone preparing for advanced studies or careers requiring strong analytical and problem-solving skills

Real-World Application

This course prepares students to apply linear algebra concepts in various real-world scenarios, whether in academic research, data analysis, economic modeling, or software engineering. Skills such as matrix factorization and understanding vector spaces are directly applicable in areas like 3D graphics programming, machine learning algorithms, and statistical data analysis.