Welcome to the course "An introduction to tensors and their decompositions"!
The entire course will be remote teaching, we will not have any contact lessons.
We meet in Zoom, starting on 19.05.2020 at 11.15.
Tensors are versatile tools for storing and organizing experimental data. Tensor decompositions are useful for isolating the essential features of the data.
In this course, we introduce the basic tools for computing with tensors. We will focus on various notions of tensor rank as well as tensor eigenvectors and eigenvalues.
Moreover, we describe the Tucker decompositions and the tensor rank decomposition.
Some details of the course:
- Credits: 5
- Part II of “An Introduction to Algebraic Statistics with Tensors” by C. Bocci and L. Chiantini.
- Chapters 1-6 of the book “Tensors: Geometry and Applications” by J. M. Landsberg.
- Chapters 1-2 of the book “Tensor Analysis - Spectral Theory and Special Tensors” by L. Qi and Z. Luo.
- Homework assignments: There will be weekly homework assignments (50% of the grade) starting from Lecture 2. Homework assignments contain exercises to be solved by hand or using the software Matlab. Please upload each homework file in PDF format.
- Final exam: The final exam (50% of the grade) consists of a slides presentation about a paper of choice involving one of the topics of the course.
Please see the list of suggested references for the oral presentation. If you are interested in giving a presentation about a paper which does not appear in the list, send your suggestion via email for approval.
Once you have chosen the topic of your presentation, we can arrange a time for the final examination.
There are two periods in which you can decide to give the final exam:
- First period: June 22 - July 3, 2020
- Second period: August 24 - September 18, 2020
- Deadline for the final examination: September 18, 2020.
- Grades: They are between 0 and 5. Grade at least 1 means that the exam has been passed.
Grade 1 is reached with a total of at least 50 points.
Grade 2 is reached with a total of at least 60 points.
Grade 3 is reached with a total of at least 70 points.
Grade 4 is reached with a total of at least 80 points.
Grade 5 is reached with a total of at least 90 points.
- Target Audience and Prerequisites: The course is targeted at advanced Bachelor, Master and Ph.D. Students in the School of Science. The only prerequisite is a course on Linear Algebra.