# Applied Linear Algebra for Data Science

7.5 credits

Syllabus, Master's level, 1TD060

A revised version of the syllabus is available.
Code
1TD060
Education cycle
Second cycle
Main field(s) of study and in-depth level
Computer Science A1F, Data Science A1F
Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
Finalised by
The Faculty Board of Science and Technology, 4 March 2021
Responsible department
Department of Information Technology

## Entry requirements

120 credits. Computer Programming II or Programming, Bridging Course. Linear Algebra II. Scientific Computing II or Scientific Computing, Bridging Course or Statistical Machine Learning. Proficiency in English equivalent to the Swedish upper secondary course English 6.

## Learning outcomes

On completion of the course, the student should be able to:

• discuss how linear algebra is used when solving problems in data science;
• explain how the most common matrix factorizations are computed numerically;
• implement and code numerical algoritms covered in the course;
• analyze algorithms' computational and memory complexity and discuss efficient implementations;
• argue for and apply linear algebra tools, such as principal component analysis, to various practical problems in data science.

## Content

The four fundamental subspaces associated with a matrix. Matrix factorization (decomposition) as a concept and idea. Least squares solutions to linear systems and applications in regression models. QR factorization, Householder and Givens rotations. Constrained least squares.

Methods for finding eigenvalues and eigenvectors (power method and QR method). Singular value decomposition (SVD) and applications. Principal component analysis and how it can be used for dimension reduction. Matrix-free metods.

Sparse storage format. Tensors and some of its applications in machine learning.

## Instruction

Lectures, problem solving, assignments.

## Assessment

Final exam (4.5hp) and assignments (3hp).

If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.