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Class notes

Module 1 Class notes calcul matriciel (mpu 1050)

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note de cours du module a de calcul matriciel (mpu1050)

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  • April 21, 2021
  • 45
  • 2019/2020
  • Class notes
  • Louis dupont
  • Module 1
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Module 1 - Notes - MPU1050


Vecteurs, calcul matriciel (Université du Québec à Trois-Rivières)




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Automne 2018




MPU1050
Vecteurs, calcul matriciel
Document rédigé par Sophie Papineau
et Alexandra Peterson
Selon les notes de Louis Dupont




Module 1

Notes de cours

Chapitre 1 : Les matrices

Chapitre 2 : Le déterminant

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Table des matières

Chapitre 1 : Les matrices 3

Définition d’une matrice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Format d’une matrice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Matrice ligne . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Matrice colonne . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Matrice carré . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Trace d’une matrice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Égalité de matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Matrice nulle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Matrices triangulaires . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Matrice diagonale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Matrice scalaire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Matrice identité . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Matrice symétrique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Matrice antisymétrique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Matrice échelonnée . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Matrice échelonnée réduite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Addition de matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Multiplication d’une matrice par un scalaire . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Matrice opposée . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Transposition d’une matrice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20


2
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