On the occasion of the 200th anniversary of the birth of Hermann Grassmann (1809-1877), an interdisciplinary conference was held in Potsdam, Germany, and in Grassmann's hometown Szczecin, Poland. The idea of the conference was to present a multi-faceted picture of Grassmann, and to uncover the complexity of the factors that were responsible for his creativity. The conference demonstrated not only the very influential reception of his work at the turn of the 20th century, but also the unexpected modernity of his ideas, and their continuing development in the 21st century. This book contains 37 papers presented at the conference. They investigate the significance of Grassmann's work for philosophical as well as for scientific and methodological questions, for comparative philology in general and for Indology in particular, for psychology, physiology, religious studies, musicology, didactics, and, last but not least, mathematics. In addition, the book contains numerous illustrations and English translations of original sources, which are published here for the first time. These include life histories of Grassmann (written by his son Justus) and of his brother Robert (written by Robert himself), as well as the paper "On the concept and extent of pure theory of number'' by Justus Grassmann (the father).

This self-contained textbook takes a matrix-oriented approach to linear algebra and presents a complete theory, including all details and proofs, culminating in the Jordan canonical form and its proof. Throughout the development, the applicability of the results is highlighted. Additionally, the book presents special topics from applied linear algebra including matrix functions, the singular value decomposition, the Kronecker product and linear matrix equations. The matrix-oriented approach to linear algebra leads to a better intuition and a deeper understanding of the abstract concepts, and therefore simplifies their use in real world applications. Some of these applications are presented in detailed examples. In several 'MATLAB-Minutes' students can comprehend the concepts and results using computational experiments. Necessary basics for the use of MATLAB are presented in a short introduction. Students can also actively work with the material and practice their mathematical skills in more than 300 exercises.

Dieses Lehrbuch uber die Lineare Algebra deckt den gesamten Stoff der zweisemestrigen Grundvorlesung ab. Seine anschauliche und konsequent matrizenorientierte Herangehensweise ermoeglicht Studierenden ein intuitives Verstandnis der abstrakten Objekte. Die im Buch prasentierten vielfaltigen Anwendungen und Beispiele motivieren Studierende zur intensiven Auseinandersetzung mit der Linearen Algebra als leistungsfahiges mathematisches Werkzeug. In vielen "MATLAB-Minuten" koennen sich Studierende wichtige Satze und Konzepte am Rechner erarbeiten. Alle notwendigen Vorkenntnisse werden in einer MATLAB-Kurzeinfuhrung erlautert. Das Buch enthalt zudem uber 350 UEbungsaufgaben, die das Erlernen des Stoffes unterstutzen. Interessierte Studierende finden daruber hinaus historische Notizen zur Entwicklung des Gebiets. Fur diese dritte Auflage wurde die zweite Auflage durchgesehen und erganzt. Zu den Erganzungen gehoeren Abschnitte uber die vollstandige Induktion und die Existenz von Basen und von Adjungierten in unendlichdimensionalen Vektorraumen. Der ubersichtliche Aufbau und das bewahrte Konzept des Lehrbuchs wurden beibehalten.

On the occasion of the 200th anniversary of the birth of Hermann Grassmann (1809-1877), an interdisciplinary conference was held in Potsdam, Germany, and in Grassmann's hometown Szczecin, Poland. The idea of the conference was to present a multi-faceted picture of Grassmann, and to uncover the complexity of the factors that were responsible for his creativity. The conference demonstrated not only the very influential reception of his work at the turn of the 20th century, but also the unexpected modernity of his ideas, and their continuing development in the 21st century.

This book contains 37 papers presented at the conference. They investigate the significance of Grassmann's work for philosophical as well as for scientific and methodological questions, for comparative philology in general and for Indology in particular, for psychology, physiology, religious studies, musicology, didactics, and, last but not least, mathematics. In addition, the book contains numerous illustrations and English translations of original sources, which are published here for the first time. These include life histories of Grassmann (written by his son Justus) and of his brother Robert (written by Robert himself), as well as the paper "On the concept and extent of pure theory of number'' by Justus Grassmann (the father).<