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- Choose an operation.
- Set the number of rows and columns and type the entries. Decimals and negative numbers are allowed.
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Formel
Matrix multiplication takes dot products of rows of A with columns of B, so A's column count must equal B's row count. Determinants and inverses use Gaussian elimination with partial pivoting for numerical stability.
(AB)ᵢⱼ = Σₖ Aᵢₖ Bₖⱼ
det(A) = product of pivots × (−1)^(row swaps)
A⁻¹ exists only if det(A) ≠ 0
2 × 2 example
- A = [[4, 7], [2, 6]].
- det(A) = 4 × 6 − 7 × 2 = 10.
- A⁻¹ = (1/10) × [[6, −7], [−2, 4]] = [[0.6, −0.7], [−0.2, 0.4]].
Häufige Fragen
Is matrix multiplication commutative?
No. In general AB ≠ BA, and one product may exist while the other doesn't.
Why can't my matrix be inverted?
A matrix with determinant 0 is singular: its rows are linearly dependent, so no inverse exists.
What is the rank of a matrix?
The number of linearly independent rows (or columns). A square n × n matrix is invertible exactly when its rank is n.