Addition
\([a_{ij}] + [b_{ij}] = [a_{ij} + b_{ij}]\)
Matriisilaskin
Suorita matriisioperaatioita kuten yhteenlasku, vähennyslasku, kertolasku, determinantti, käänteismatriisi, transpoosi ja ominaisarvojen laskenta
Tulokset
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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)