Addition
\([a_{ij}] + [b_{ij}] = [a_{ij} + b_{ij}]\)
Calculatrice de matrice
Effectuer des opérations matricielles incluant l'addition, la soustraction, la multiplication, le déterminant, l'inverse, la transposée et le calcul des valeurs propres
Résultats
Entrez les valeurs et cliquez sur Calculer pour voir le résultat.
Theory & Formula
A matrix is a rectangular array of numbers arranged in rows and columns. Matrix algebra is fundamental to linear algebra, computer graphics, and many scientific applications.
Key operations:
- Addition/Subtraction: Matrices must have same dimensions
- Multiplication: (m×n) × (n×p) = (m×p), rows of A must equal columns of B
- Determinant: Only for square matrices, measures "volume scaling"
- Inverse: A⁻¹A = I, only exists if det(A) ≠ 0
- Transpose: Flip rows and columns (Aᵀ)ᵢⱼ = Aⱼᵢ
- Eigenvalues: λ values where Av = λv for some vector v
\(A, B \in \mathbb{R}^{m \times n}\)
Worked Examples
Multiplication
\(C = AB: c_{ij} = \sum_k a_{ik}b_{kj}\)
Determinant
\(\det\begin{pmatrix}a & b \\ c & d\end{pmatrix} = ad - bc\) (2×2 case)