Lina - 3.2 Matrizen at Universität Hamburg

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Study with flashcards and summaries for the course Lina - 3.2 Matrizen at the Universität Hamburg

Exemplary flashcards for Lina - 3.2 Matrizen at the Universität Hamburg on StudySmarter:

F j
   i

Exemplary flashcards for Lina - 3.2 Matrizen at the Universität Hamburg on StudySmarter:

M A
    B

Exemplary flashcards for Lina - 3.2 Matrizen at the Universität Hamburg on StudySmarter:

Allgemeine lineare Gruppe

Exemplary flashcards for Lina - 3.2 Matrizen at the Universität Hamburg on StudySmarter:

Invertierbare Matrix

Exemplary flashcards for Lina - 3.2 Matrizen at the Universität Hamburg on StudySmarter:

Ring quadratischer Matrizen

Exemplary flashcards for Lina - 3.2 Matrizen at the Universität Hamburg on StudySmarter:

Einheitsmatrix

Exemplary flashcards for Lina - 3.2 Matrizen at the Universität Hamburg on StudySmarter:

Transponierte einer Matrix

Exemplary flashcards for Lina - 3.2 Matrizen at the Universität Hamburg on StudySmarter:

Skalar Multiplikation einer Matrix

Exemplary flashcards for Lina - 3.2 Matrizen at the Universität Hamburg on StudySmarter:

Summe zweier (mxn) Matrizen

Exemplary flashcards for Lina - 3.2 Matrizen at the Universität Hamburg on StudySmarter:

Multiplikation zweier Matrizen

Exemplary flashcards for Lina - 3.2 Matrizen at the Universität Hamburg on StudySmarter:

Darstellende Matrix für Drehung eines Vektors

Exemplary flashcards for Lina - 3.2 Matrizen at the Universität Hamburg on StudySmarter:

Multiplikation von Matrix mit Vektor

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Exemplary flashcards for Lina - 3.2 Matrizen at the Universität Hamburg on StudySmarter:

Lina - 3.2 Matrizen

F j
   i

V->W mit
Fji(vk) := wj für k=1, 0 sonst
Basis von Hom(V, W) 

Lina - 3.2 Matrizen

M A
    B

A, B zwei geordnete Basen von Vektorräumen
Jede lineare Abbildung zwischen diesen VR hat eine Matrix A mit
¢(vj) =Summe i=1 bis M von aij*wi
MAB: Hom(V, W) – > M(mxn, K)
¢ l-> A = MAB
Matrix Ab(¢) stellt lineare Abbildung bezüglich der geordneten Basen dar

Lina - 3.2 Matrizen

Allgemeine lineare Gruppe

Menge GL(n, K) := Alle invertierbaren nxn Matrizen
Und Verknüpfung Multiplikation
Neutrales Element Einheitsmatrix

Lina - 3.2 Matrizen

Invertierbare Matrix

A*A’=A’*A=En

Lina - 3.2 Matrizen

Ring quadratischer Matrizen

Mit addition und Multiplikation als Operationen
Hom(K^n, K^n) – > M(n n, K)

Lina - 3.2 Matrizen

Einheitsmatrix

1 auf der Diagonale, sonst 0

Lina - 3.2 Matrizen

Transponierte einer Matrix

1. Zeile wird zu 1. Spalte,… 

Lina - 3.2 Matrizen

Skalar Multiplikation einer Matrix

Jede Komponente wird mit dem Skalar multipliziert

Lina - 3.2 Matrizen

Summe zweier (mxn) Matrizen

Komponentenweise addieren

Lina - 3.2 Matrizen

Multiplikation zweier Matrizen

1.Zeile 1.Spalte der Lösungsmatrix ist 1Z1S*1Z1S+1Z2S*2Z1S+1T3S*3S1Z…

Lina - 3.2 Matrizen

Darstellende Matrix für Drehung eines Vektors

cos ß   – sin ß
sin ß       cos ß

Lina - 3.2 Matrizen

Multiplikation von Matrix mit Vektor

Zeile (der Matrix) mal Spalte (des Vektors) 

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