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Prof. Wolfgang Ertel
Wolfgang Ertel
Professor Dr. rer. nat.

Applied Linear Algebra and Analysis (ALAA)

for up to date information on dates and organisation please refer to the LSF-Page


Courses of studies Master IN, MM, EI
Professor Ertel, Schneider, Bou Ammar
Requirements Basics in mathematics, programming
Evidence of academic achievement 24. Sep. 16:30 - 17:30, 1. Oct. 17:00 - 17:30 (90 min.)

Course Objectives:

This is a preparatory course for master students. The goal is to close gaps in the required bachelor mathematics in order to prepare the students for the lecture "Advanced mathematics for Engineers". In 28 hours of lectures we provide the essentials of Linear Algebra and multidimensional Analysis and in another 28 hours these subjects will be practiced by solving exercises.

Most of the lectures will be given through videos from the MIT open course ware platform. This means you will be getting excellent lectures from one of the best Professors in the world! Additionally, during the course a lecturer who can interrupt the videos at any time to answer questions will be present.

The course takes seven days with eight hours per day. On all seven days the first four hours, in the morning (9:00 to 12:30), will include lectures and the second four hours, in the afternoon (14:00 to 17:30), will be dedicated to the practical solution of exercises and asking questions. We strongly recommend all students to attend this preparatory course.


Day 1: LU-decomposition, Inverses and Transposes, Column Spaces and NullSpaces
Day 2: Ax = 0 and Pivot Variables, Solving Ax = b, The Four Fundamental Subspaces
Day 3: Orthogonality, Gram Schmidt technique, Determinants, Properties of Determinants
Day 4: Eigenvalues and Eigenvectors, Diagonalization of Matrices
Day 5: Symmetric and Positive Semi-Definite Matrices, Similar Matrices and Jordan Form, Linear Transformation
Day 6: Taylor-Series, Basics of multidimensional Analysis
Day 7: Multidimensional Nonlinear Optimization

Video lectures:

Lec # Topics Date
1 The geometry of linear equations day 1
2 Factorization into A = LU day 1
3 Transposes, Permutations, Spaces R^n day 1
4 Column Space and Nullspace day 1
5 Solving Ax = 0: Pivot Variables, Special Solutions day 2
6 Solving Ax = b: Row Reduced Form R day 2
7 Independence, Basis, and Dimension day 2
8 The Four Fundamental Subspaces day 2
9 Orthogonal Vectors and Subspaces day 3
10 Projections onto subspaces day 3
11 Orthogonal Matrices and Gram-Schmidt day 3
12 Properties of Determinants day 3
13 Determinant Formulas and Cofactors day 4
14 Cramer's rule, inverse matrix, and volume day 4
15 Eigenvalues and Eigenvectors day 4
16 Diagonalization and Powers of A day 4
17 Symmetric Matrices and Positive Definiteness day 5
18 Similar Matrices and Jordan Form day 5
19 Linear Transformations and Their Matrices day 5
20 Change of basis; image compression day 5


Solutions : Linear Algebra, Analysis Part 1