Matrix Methods in Data Science - Einzelansicht

Please register on moodle for the course Mach, Th.: Matrix Methods in Data Science (https://moodle2.uni-potsdam.de/course/view.php?id=38490). The key is svd.

There is no single textbook for the course. Possible references include:

[1] E. Darve and M. Wootters, Numerical Linear Algebra with Julia, vol. 172, SIAM, 2021.
[2] J. W. Demmel, Applied Numerical Linear Algebra, SIAM, 1997.
[3] G. Strang, Linear Algebra and Learning from Data, Welesely Cambridge Press, 2019 (unfortunately not available in the library, not available online; the library of TU Berlin has several copies)
[4] L. N. Trefethen and D. Bau, III., Numerical Linear Algebra, SIAM, Philadelphia, 1997.
[5] D. S. Watkins, Fundamentals of Matrix Computations, vol. 64, John Wiley, 2004.

This course requires a solid understanding of Linear Algebra, typically taught over two semesters with the second part sometimes called matrix theory, and of numerical methods (interpolation, rounding errors, Newton's method, numerical integration, solving linear systems with Gaussian elimination and with iterative methods, as well as the QR eigenvalue algorithm).

Studierende des Bachelor Mathematik sollten
Basismodul Lineare Algebra und Analytische Geometrie I,
Basismodul Lineare Algebra und Analytische Geometrie II,
Aufbaumodul Computermathematik, and
Aufbaumodul Numerik II
erfolgreich bestanden haben.

There will be an in person oral exam at the end of the term, if regulations permit. To qualify for the exam you have to achieve at least 50% of the points in the homework assignments.

The following topics, among others, will be covered in this course:

• matrix functions, with applications to graph centrality, and Krylov subspace methods,
• the main matrix decompostions: Schur decomposition, singular value decomposition, QR decomposition, CUR, NMF,
• large strutured and sparse matrices, including links to Kronecker products and matrix equations,
• tensor methods, and
• their applications and more.

This course is aimed for students interested in data science, matrices, and numerical computations.The course teaches (numerical) linear algebra methods and applies them to data science problems.
Matrix methods in data science is an evolution of numerical linear algebra, which was offered in the summer term 2022. Due to the significant overlap we'll exclude students who have successfully passed numerical linear algebra in the past.

Für Studierende Mathematik Lehramt empfehlen wir zunächst die Lehrveranstaltung Numerik II, welche im Sommersester auf Deutsch angeboten wird und verwandte Themen behandelt, zu besuchen.