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Calcul matriciel et systèmes linéaires

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< Calcul Matriciel

Calcul Matriciel

Définitions de base

Une matrice de taille m×n est un tableau de nombres disposés en m lignes et n colonnes.

Types de matrices

Matrice carrée (m = n)
Matrice diagonale (a_ij = 0 si i ≠ j)
Matrice identité I_n (diagonale avec 1 sur la diagonale)
Matrice triangulaire (supérieure ou inférieure)

Opérations fondamentales

Addition (matrices de même taille)
Multiplication par un scalaire
Produit matriciel (nombre de colonnes de A = nombre de lignes de B)

Systèmes Linéaires

Systèmes d'Équations Linéaires

Forme générale

Un système de m équations à n inconnues s'écrit :

a₁₁x₁ + ... + a_1nx_n = b₁
...
a_m1x₁ + ... + a_mnx_n = b_m

Écriture matricielle

AX = B où :

A est la matrice des coefficients
X est le vecteur colonne des inconnues
B est le vecteur colonne des termes constants

📅 Calendrier

📝 Tâches Scolaires

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