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12. Vl Ana1LinA Matrizen $3.35   Add to cart

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12. Vl Ana1LinA Matrizen

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Dies ist eine vollständige Vorlesungsmitschrift zur zwölften Vorlesung des Moduls Analysis I und lineare Algebra für Ingenieurswissenschaften. In dieser Vorlesung wird das Thema Matrizen eingeführt. Dafür werden die elementaren Rechenoperationen für Matrizen, die Inverse, die Transponierte un...

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  • January 30, 2023
  • 9
  • 2022/2023
  • Class notes
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Matrix

Ziel Lösen von Gleichungssystemen


2B 2x t 3 2 5
2
1

Idee Schreibe System durch Matrizen


E THE
Definition Matrix

Für Zahlen
aig E Ik i 1 mi je 1 n heißt das Zahlenschena

an F
Aja an Tai Taijijae im

ii
in



m X n Matrix mit Einträgen in K
L
m Zeilen In Spalten

wenn man quadratische Matrix


Menge aller m x n Matrizen mit Einträgen in K bezeichnetdurch 1k



Bemerkung

1 i ZeileSpalt
j
2 kürzere Bezeichnung m x n Matrix über 1K

3
aig statt an
manschreibt


Bsp 1
A E ER
z B an 3
2 Nallmatrix
O Eo EN
0mn
E

, 3 Einheitsmatrix




7 In ist immer quadratisch

4 Sei mit d h ein Zeilenweltor

z B 2 i 1 3 5 E


5 Sei n 1 d h ein Spaltenrektar


z B
f ER

Rechenoperationen




A Tag B b E 1K
nur Matrizen mitgleicher Größe
At B Tag bij Ekhn dürfen addiertwerden


Skalarmultiplikation
X Elk

JA Ea Elk

Bsp 1 A
F 23J
ER B
I 1 ER


At B Ü 3 4 ER
2 2B EI G 4 ER

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