Lehrbuch Der Algebra: Unter Einschluß Der Linearen Algebra, Teil 2
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Das "Lehrbuch der Algebra" dient der Einfiihrung in die Algebra, einschliefi- lich derjenigen Teile der Algebra, die gemeinhin als Lineare Algebra bezeich- net werden. Mit dem zweiten Band legen wir nunmehr den Hauptteil des Buches vor. Den Studierenden werden zunachst die drei mittleren Kapitel VIII, IX und X interessieren, die Lineare Operatoren, Dualitat und Multilineare Algebra behandeln und damit den Stoff vermitteln, der den Kern der Anfanger- Vorlesungen iiber (Lineare) Algebra und Geometrie ausmacht und in weitem Mafie auch in den parallelen Analysis-Vorlesungen gebraucht wird. Zur Untersuchung linearer Operatoren in Kapitel VIII sind einige Ergeb- nisse iiber Polynomringe notig, die in Kapitel VII, welches allgemeine Be- griffe der Kommutativen Algebra vorstellt, enthalten sind, wenn sie auch nur einen gering en Teil dieses Kapitels bilden, den der Leser aber an Hand kurzer Bemerkungen zu Beginn der einzelnen Paragraphen unschwer her- ausfinden wird. Dem Leser sei geraten, sich hier anfangs auf das Notige zu beschranken. Weiter empfehlen wir dem Leser, sich friihzeitig mit dem Tensorprodukt als dem Grundbegriff multilinearer Algebra vertraut zu machen; hierzu bieten schon einige Stellen der Kapitel VIII und IX Gelegenheit. Systematisch wird das Tensorprodukt erst in Kapitel X besprochen, jedoch ergeben die ersten Paragraphen 80 und 81 dieses Kapitels eine in sich geschlossene einfach gehaltene Einfiihrung, die man leicht vorziehen kann. Die Paragraphen 80 und 84 konnen librigens ohne wei teres als Teil des Kapitels VI liber Determinanten in den erst en Band aufgenommen werden.
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