Entry requirements

120 credits. Computer Programming II or Programming, Bridging Course. Linear Algebra II. One of Introduction to Scientific Computing, Scientific Computing II, 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. Sparse storage format. Solving large linear systems with LU-factorization and other factorizations (LDL and Cholesky). Iterative methodhs for large linear systems. The Krylov subspace and Krylov subspace methods, for example Arnoldi, Conjugate Gradient, Lanczos and GMRES.  QR factorization, Householder and Givens rotations. Constrained least squares.

Singular value decomposition (SVD), pseudoinvers and applications. Principal component analysis and how it can be used for dimension reduction.

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.