Prof. :  Klaus Diepold 
Teaching Assistants:  Sven Gronauer, Simon Schumann 
Contact  tvsc.ldv@xcit.tum.de 
Target Group:  Master level students in technical fields 
ECTS:  6 Credits 
Contact Hours:  3 SWS 
Turnus:  Winter term 
Registration:  via TUMOnline (necessary to get access to course materials on Moodle) 
Time & Place:  Wednesdays, 09:4512:15, Room Z995 
Start:  October 18th, 2023 
Registration and Prerequisites
 No preregistration necessary
 Working knowledge of (Numerical) Linear Algebra and Matlab.

 Check out the writeup on mathematical preliminaries as a quick reference to review the knowledge that we require for this course.
Contents
A broad range of engineering problems involve the solution of large systems of linear equation or other linear algebra computations involving large matrices. This includes finding the best search result using Google’s “PageRank” technology to designing largescale integrated semiconductor circuits. Other signal processing tasks can also be represented in this way. We mostly assume the linear systems to be timeinvariant. This assumption enables us to use traditional tools in system modeling such as computing the response of a system in the frequencydomain (using FFTs) or using the ztransform.
However, there are systems where the property of timeinvariance is not satisfied and where frequencydomain operations are no longer feasible. The purpose of this course is to introduce an alternative way to treat linear systems that generalizes also to timevarying systems. Linear Systems will be described in terms of a statespace realization, which uses concepts of linear algebra. The course emphasizes the representation of largescale computational problems (matrixvector multiplication, matrix inversion, matrix factorization, etc.) as problems of timevarying linear systems. This approach allows that engineers can apply linear system based thinking to design fast and efficient numerical algorithms for largescale linear algebra problems.
Students will work in teams on project tasks, developing Matlab using the techniques covered in the class. The course will instruct students to work in an agile work style to software development supported by modern, stateoftheart software tools.
Reference Literature:
 P. Dewilde, K. Diepold, A.J. van der Veen. Systems and Computations. 2018. Preprint available on Moodle.
 P. Dewilde, A.J. van der Veen. TimeVarying Systems and Computations. Kluwer Academic Publishers, 1998.
The background mathematical knowledge (also covered in exercise) is available in:
 G. Strang. Linear Algebra and its Applications. Hartcourt Brace Jovanovich Publishers, San Diego, 1988.
Grade Structure
Final Examination (Oral) 50%; Homework and Project 50%.