Addition
\([a_{ij}] + [b_{ij}] = [a_{ij} + b_{ij}]\)
行列計算機
行列の演算を行う：加算、乗算、行列式、逆行列
結果
値を入力して、計算をクリックすると結果が表示されます。
理論と公式
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
\(A, B \in \mathbb{R}^{m \times n}\)
解説付き例題
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)