Lehrbuch Der Linearen Algebra
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Das vorliegende Buch ist aus einer Grundvorlesung �ber lineare Algebra hervorgegangen, die ich an der Universit�t Bern mehrmals gehalten habe. Diese Vorlesung ist f�r Studenten des zweiten Hochschulsemesters bestimmt, und zwar sowohl f�r solche, die Mathematik als Hauptfach studieren, wie auch f�r Nebenfachmathematiker. Bei den letzteren handelt es sich vor allem um Ver- sicherungsmathematiker, Astronomen, Physiker und Chemiker, denen sich . gelegentlich auch mathematisch interessierte Volkswirtschaftler angeschlossen haben. Aus der Verschiedenartigkeit der H�rer ergab sich vorerst die Not- wendigkeit, die Vorlesung m�glichst voraussetzungslos aufzubauen, was auch im Buch zum Ausdruck kommt. Vorausgesetzt wird die durch das Gymnasium vermittelte mathematische Bildung und die F�higkeit zu abstraktem Denken. W�nschenswert ist die Kenntnis der vektoriellen Geometrie, da sie wertvolles Anschauungsmaterial f�r die allgemeine Theorie liefert. Sodann mu te der Inhalt der Vorlesung auf das Wichtigste beschr�nkt bleiben, weshalb auch im Buch nur die reellen und komplexen Vektorr�ume betrachtet werden, mit Ausnahme des letzten Kapitels. Schlie lich werden auch die Anwendungen der linearen Algebra ber�ck- sichtigt, entsprechend den Bed�rfnissen der meisten H�rer. Neben Einzel- heiten der Stoffauswahl kommt dies vor allem darin zum Ausdruck, da f�r die wichtigsten Problemklassen der numerischen linearen Algebra jeweils ein einfaches Rechenverfahren erkl�rt wird. Da dabei auf Vollst�ndigkeit ver- zichtet werden mu , versteht sich von selbst. Nicht allgemein �blich ist die Behandlung der linearen Programmierung, der Ausgleichung nach Tschebyscheff und der Spieltheorie in einem Lehrbuch der linearen Algebra. Ich habe diese Sachgebiete in der Form vonEinf�hrungen aufgenommen, weil es sich um immer wichtiger werdende Teile der linearen Algebra handelt.
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