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Skript: Lineare Algebra II

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Author(s): A. Kresch
Series: lecture notes
Edition: version 2020-09-02
Year: 2020

Language: German
Commentary: Downloaded from the web; no longer available

1
Elementare Modultheorie mit Anwendungen
1
1.1
Endlich erzeugte Moduln über euklidischen Ringen . . . . . . . . . .
1
1.2
Anwendungen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
1.3
Kommutierende Blockmatrizen
. . . . . . . . . . . . . . . . . . . . .
10
2
Bilinearformen
12
2.1
Metrik und Norm . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12
2.2
Euklidische Vektorräume . . . . . . . . . . . . . . . . . . . . . . . . .
13
2.3
Unitäre Vektorräume . . . . . . . . . . . . . . . . . . . . . . . . . . .
22
2.4
Bilinearformen und Matrizen
. . . . . . . . . . . . . . . . . . . . . .
25
2.5
Selbstadjungierte Endomorphismen . . . . . . . . . . . . . . . . . . .
32
3
Multilineare Algebra
34
3.1
Das Tensorprodukt . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35
3.2
Der Dualraum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
39
3.3
Symmetrische und äussere Potenz . . . . . . . . . . . . . . . . . . . .
41