Lineare Algebra Und Analytische Geometrie: Band III Aufgaben Mit Lösungen
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18. 2 Die euklidische Normalform einer Quadrik 18. 3 Euklidische Quadrikengeometrie 18. 4 Metrische Klassifikation der Quadriken im E2 und E3 Kapitel 6: Projektive Geometrie 19 Der n-dimensionale projektive Raum 19. 1 Motivation 2 19. 2 Das Leitbild der projektiven Ebene P 19. 3 Der n-dimensionale projektive Raum pn 19. 4 Projektive Unterraume 19. 5 Dimensionssatz fUr projektive Unterraume 19. 6 Projektive Koordinaten 19. 7 Gleichungen und Parameterdarstellungen projektiver Unterraume 19. 8 Projektive Koordinatentransformationen 20 Projektive Abbildungen 20. 1 Problemstellung 20. 2 Eigenschaften projektiver Abbildungen 20. 3 Koordinatendarstellung projektiver Abbildungen 20. 4 Projektive Selbstabbildungen 20. 5 . Projektivitaten und Perspektivitaten 20. 6 Projektionen 20. 7 Das Doppelverhaltnis 20. 8 Beziehungen zwischen projektiven und affinen Raumen 21 _. . .:: D;.::: a: ;s: . ., . .: D: .;u:: .: a:: . l=i. .: t. =a: . .: t:: s: ., sp: .: r:, .;1: . .: - n:: z=i. t:: p 21. 1 Gru dbegriffe der dual en Vektorraume 21. 2 Das Dualitatsprinzip der linearen Algebra 21. 3 Das Dualitatsprinzip der projektiven Geometrie 21. 4 Hyperebenenkoordinaten 21. 5 Das Doppelverhaltnis von Hyperebenen 21. 6 Dualit t bei projektiven Abbildungen 22 Kollineationen und Korrelationen 22. 1 Kollineationen 22. 2 Der v. STAUDTsche Satz 22. 3 Korrelationen 22. 4 Polarsysteme und Nullsysteme 23 Standardsatze der projektiven Ebene p2 23. 1 Satz von PAPPUS. Vollstandiges Vierseit, vollstandiges Viereck 23. 2 Der Satz von DESARGUES 23. 3 Der Satz von PAPPUS-PASCAL 24 Projektive Quadrikentheorie 24. 1 Begriff der Quadrik im pn 24.
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