Lina 2.3 Vektorräume at Universität Hamburg

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Study with flashcards and summaries for the course Lina 2.3 Vektorräume at the Universität Hamburg

Exemplary flashcards for Lina 2.3 Vektorräume at the Universität Hamburg on StudySmarter:

Vektorraum (Axiome) 

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Vektoren

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Nullvektor

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Skalare

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Vektoraddition

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Vektormultiplikation

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Nullvektorraum

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Untervektorraum 

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Annihilator

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Triviale Untervektorraum

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Der Schnitt zweier UVR

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Linearkombination

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Exemplary flashcards for Lina 2.3 Vektorräume at the Universität Hamburg on StudySmarter:

Lina 2.3 Vektorräume

Vektorraum (Axiome) 

(Menge, zwei Verknüpfungen)

  • Addition ist abelsche Gruppe
  • Multiplikation assoziativ
  • Distributivgesetze
  • Neutrales Element der Multiplikation

Lina 2.3 Vektorräume

Vektoren

Elemente des Vektorraumes

Lina 2.3 Vektorräume

Nullvektor

Neutrales Element der Vektormultiplikation

Lina 2.3 Vektorräume

Skalare

Elemente aus K im K-Vektorraum

Lina 2.3 Vektorräume

Vektoraddition

Komponentenweise

Lina 2.3 Vektorräume

Vektormultiplikation

Mut Skalar
Komponentenweise Multiplikation

Lina 2.3 Vektorräume

Nullvektorraum

({0V}, +, *) 

Lina 2.3 Vektorräume

Untervektorraum 
  • Nicht leer
  • Teilmenge eines Vektorraumes
  • Unter beiden Verknüpfungen abgeschlossen

Lina 2.3 Vektorräume

Annihilator

Untervektorraum, der alle Abbildungen von einer Menge nach K enthält, sodass für alle eingesetzten Werte aus der Teilmenge das Ergebnis null ist

Lina 2.3 Vektorräume

Triviale Untervektorraum

Untervektorraum, der nur die Null enthält

Lina 2.3 Vektorräume

Der Schnitt zweier UVR

Ist wieder UVR

Lina 2.3 Vektorräume

Linearkombination

Endlich viele Vektoren, die nicht unbedingt verschieden sein müssen
Ein Element w heißt Linearkombination, wenn des aus der Summe der Skalar multiplizieren Vektoren besteht
W= l1 1 + l2v2 +… + lnvn

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