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:

Enthällt eine Familie den Nullvektor

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Leere Familie

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Linear abhängige Teilfamilien

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Linear unabhängige Familie

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Geordnete Familie

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Durch natürliche Zahlen indizierte Familie

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Indexmenge

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Familie

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Der Span ist 

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Von einer Teilmenge aufgespannter Raum

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Erzeugnis

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

Lina 2.3 Vektorräume

Enthällt eine Familie den Nullvektor

So ist sie linear abhängig

Lina 2.3 Vektorräume

Leere Familie

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Linear unabhängig 

Lina 2.3 Vektorräume

Linear abhängige Teilfamilien

Familie von Vektoren ist linear unabhängig, wenn jede Teilmenge linear unabhängig ist

Lina 2.3 Vektorräume

Linear unabhängige Familie

Die Linearkombination ergibt nur dann null, wenn alle Indizes Null sind

Lina 2.3 Vektorräume

Geordnete Familie

Struktur durch Indizierung mit natürlichen Zahlen

Lina 2.3 Vektorräume

Durch natürliche Zahlen indizierte Familie

Ordnung auf Indexmenge -> Ordnung der Familie

Lina 2.3 Vektorräume

Indexmenge

Menge, die Familie indiziert

Lina 2.3 Vektorräume

Familie

Abbildung von A->M
Durch A indiziert Familie
A ist Indexmenge
A ist die Menge aus der die Skalare für die Linearkombination kommen

Lina 2.3 Vektorräume

Der Span ist 

Ein UVR 

Lina 2.3 Vektorräume

Von einer Teilmenge aufgespannter Raum

Wenn alle Vektoren aus einer Teilmenge kommen

Lina 2.3 Vektorräume

Erzeugnis

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Lina 2.3 Vektorräume

Span

Menge aller Linearkombinationen
Von den Vektoren aufgespannter Raum
Erzeugnis

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