Advanced linear algebra II

MATH-115(b) / coefficient 6

Teacher: Janzer Oliver

Language: English

Summary

The aim of the course is to introduce the basic concepts of linear algebra and to rigorously prove the subject's main results.

Content

  • Further study of endomorphism structure and Jordan canonical forms.
  • Dual space and bilinear forms, pairing between vector spaces, quadratic forms.
  • Inner products, orthonormal bases, orthogonal projections, isometries, orthogonal matrices, spectral theorem (first version).
  • Pseudo-Euclidean spaces, Sylvester's theorem, Lorentz-Minkowski spacetime and special relativity.
  • Hermitian forms, Hermitian spaces, self-adjoint and normal operators, spectral theorem (second version), unitary group, an overview of quantum mechanics.
  • Basic concepts of tensors.

Keywords

Inner product, bilinearity, orthogonality, reduction of endomorphisms, Jordan basis, self-adjoint operators.

Learning Prerequisites

Required courses

Algèbre Linéaire avançée 1

Important concepts to start the course

Fundamentals of linear algebra from the first semester.

Teaching methods

Lectures and in-class exercises.

Expected student activities

Understanding the course material, solving exercises.

Assessment methods

Written exam.

Supervision

Office hours No
Assistant.e.s Yes
Forum Yes

Resources

Notes/Handbook

Lecture notes will be provided.

Moodle Link

In the programs

  • Semester: Spring
  • Exam form: Written (summer session)
  • Subject examined: Advanced linear algebra II
  • Courses: 3 Hour(s) per week x 14 weeks
  • Exercises: 3 Hour(s) per week x 14 weeks
  • Type: mandatory

Reference week

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