Linear algebra

Serge RICHARD Professor

Department: G30

Class Time: 2015 Spring Tuesday
Recommended for: 1st year, 1st and 2nd semesters

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Course Overview

Linearity is one of the most basic concepts for handling quantities in current natural sciences. Indispensable in quantum mechanics and relativity, its use has spread across all branches of natural sciences and beyond. Linear algebra, developed in the Nineteenth century, is the mathematical theory of linearity.

The first half of this one-year course focuses on the techniques for manipulating systems of linear equations and their application to analytic geometry (in arbitrary dimensions). The second half focuses on a deeper study of linear maps (composition, invertibility, eigenvectors and eigenvalues...). The notions of scalar product and determinant will also be studied, and the semester will end with an introduction to complex numbers.

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There is no homework for this course. However, you are strongly encouraged to do all homework problems assigned to you during the linear algebra part of the Mathematics Tutorial II.


Quizzes will be given randomly during the classes. They will not be announced.


  • It is expected that you attend all lectures.
  • All electronic devices have to be turned off and are prohibited on the tables.
  • Prepare for class by
    1. reviewing previously learned concepts from previous lectures
    2. completing the homework problems assigned in Mathematics Tutorial II.
  • The instructor is here to help you. Please do not hesitate to contact me, earlier rather than later.

Grading Policy

Your final grade will be determined by quizzes (30%), the midterm exam (30%) and the final exam (40%).

The grading scale will be S: 90-100, A: 80-89, B: 70-79, C: 60-69, F: 0-59

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Lecture Notes

Linear algebra (full document, 130 pages) (PDF, 432KB)

Cover (PDF, 15KB)
Contents (PDF, 35KB)
Introduction (PDF, 76KB)
Chapter 1
Geometric setting (PDF, 137KB)
Chapter 2
Matrices and linear equations (PDF, 149KB)
Chapter 3
Vector spaces (PDF, 119KB)
Chapter 4
Linear maps (PDF, 136KB)
Chapter 5
Scalar product and orthogonality (PDF, 89KB)
Chapter 6
The determinant (PDF, 107KB)
Chapter 7
Eigenvectors and eigenvalues (PDF, 124KB)
Chapter 8
Applications (PDF, 105KB)
Chapter 9
Complex numbers (PDF, 87KB)

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Page last updated August 11, 2015

The class contents were most recently updated on the date indicated. Please be aware that there may be some changes between the most recent year and the current page.

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