Mini Course: Matrix Eigendecomposition

In linear algebra, eigendecomposition or sometimes spectral decomposition is the factorization of a matrix into a canonical form, whereby the matrix is represented in terms of its eigenvalues and eigenvectors. 

Eigendecomposition has a huge number of applications in science: solving linear differential equations, image analysis, machine learning, quantum mechanics, statistics and more.

In this course, we will cover the basics of the technique and motivate it by introducing a number of scientific applications. This course will be designed in a flipped classroom method, where the theory will be introduced in short videos and the in-person sessions will cover exercises and applications.

Target audience

This course is suitable for anyone. There will be some programming for exercises, but participant experience will be expected to be low.


The teachers will be Vsevolod "Seva" Nikulin (PhD Student) and Jeremie Gillet (eigendude). 


The details of the course are as follow.

Some hands-on exercises will involve some programming in Python with Jupyter notebooks, but expectations of participants experiences will be kept low.

Date Time Topic Video Teacher
Monday, June 28 10AM-12PM Definitions, motivation, computation, geometric transformations Session 1 (9:28) Jeremie 
Thursday, July 1 10AM-12PM Principal Component Analysis, Spectral clustering Session 2 (9:02) Seva
Monday, July 5 10AM-12PM Ordination methods, solving differential equations, quantumpPhysics applications, Singular Value Decomposition N/A Jeremie
Thursday, July 8 10AM-12PM Eigenvector centrality, Google Pagerank N/A Seva

You will find all the material used during this course here.

The sessions were recorded here: session 1session 2session 3session 4.

More information

  • Location: B701, Computer Lab, Lab 3.
  • What to bring:
    • Note-taking material
    • A laptop with Anaconda installed (or access to Deigo)
  • Zoom link: if you prefer joining remotely, or if B701 exceeds 50% capacity, you can join using this link. Unfortunately, we won't be able to provide much help with the hands-on part via Zoom. 
  • Video Recording: this course might be recorded and uploaded online, only the teacher will be recorded. Contact Jeremie Gillet if you have reservations about this.
  • Drinks: There will be free coffee and tea, bring your cup!

If you are interested in the course but cannot participate to this particular event, let us know and we will contact you for any later occurrence of this course.

Thank you very much for your interest.

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Have you studied Matrix Algebra and Eigendecomposition before? How comfortable are you with it? Do you use it in your research?
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