Jörg Liesen's research interests are in Numerical Linear Algebra, Matrix Theory, Constructive Approximation, and Computational Complex Analysis. A particular focus of his work is the convergence and stability analysis of iterative methods for solving large linear algebraic problems, which occur throughout science and engineering applications. He is also interested in the history of Mathematics, and in particular of Linear Algebra. He is the recipient of several prizes and awards for his mathematical work, including the Householder Award, the Emmy Noether Fellowship and the Heisenberg Professorship of the DFG. He likes to teach and pursue Mathematics as a lively subject, connecting theory with an ever-increasing variety of fascinating applications.

Volker Mehrmann's research interests are in Numerical Mathematics, Control Theory, Matrix Theory, Mathematical Modeling as well as Scientific Computing. In recent years he has focused on the development and analysis of numerical methods for nonlinear eigenvalue problems and differential-algebraic systems of port-Hamiltonian structure with applications in many fields such as mechanical systems, electronic circuit simulation and acoustic field computations. He is co-editor-in-chief of the journal Linear Algebra and its Applications and editor of many other journals in Linear Algebra and Numerical Analysis. He believes that Mathematics has become a central ingredient for the societal development of the 21st century and that mathematical methods play the key role in the modeling, simulation, control and optimization of all areas of technological development.

Anschauliche und konsequent matrizenorientierte Herangehensweise für ein intuitives Verständnis

Mit MATLAB-Übungen, in denen Studierende sich wichtige Sätze und Konzepte am Rechner erarbeiten können

Präsentiert verschiedenste moderne Anwendungen und Praxisbeispiele

Lineare Algebra im Alltag.- Mathematische Grundbegriffe.- Algebraische Strukturen.- Matrizen.- Die Treppennormalform und der Rang von Matrizen.- Lineare Gleichungssysteme.- Determinanten von Matrizen.- Das charakteristische Polynom und Eigenwerte von Matrizen.- Vektorräume.- Lineare Abbildungen.- Linearformen und Bilinearformen.- Euklidische und unitäre Vektorräume.- Adjungierte lineare Abbildungen.- Eigenwerte von Endomorphismen.- Polynome und der Fundamentalsatz der Algebra.- Die Jordan- und Frobenius-Normalform.- Matrix-Funktionen und Differenzialgleichungssysteme.- Spezielle Klassen von Endomorphismen.- Die Singulärwertzerlegung.- Das Kronecker-Produkt und lineare Matrixgleichungen.- Anhang A: MATLAB Kurzeinführung.- Anhang B: Matrixzerlegungen.- Anhang C: Das griechische Alphabet.