Matrix calculator (up to 4 × 4)
Type each matrix row by row: numbers in a row separated by spaces, rows by “;” or a new line.
Result
2 × 2Result size (rows × columns)
- Row 1
- [ 0.6 -0.7 ]
- Row 2
- [ -0.2 0.4 ]
- Determinant
- 10
- Condition number (1-norm)
- 14.3
Inputs
- Operation
- Inverse of A
- Matrix A
- 4 7; 2 6
How it is calculated
Sum and difference: entry by entry, both matrices must have the same size.
Result
Result size (rows × columns)
- Row 1
- [ 0.6 -0.7 ]
- Row 2
- [ -0.2 0.4 ]
- Determinant
- 10
How it is calculated
- Sum and difference: entry by entry, both matrices must have the same size.
- Product A × B: the number of columns of A must equal the number of rows of B.
- Determinant and inverse by Gauss–Jordan elimination with partial pivoting.
- Condition number = ‖A‖₁ × ‖A⁻¹‖₁: the larger it is, the less reliable the inverse.
Example
A = [4 7; 2 6]: determinant 10, inverse [0.6 −0.7; −0.2 0.4], condition number 14.3.
Good to know
- Maximum size 4 × 4. Every row must have the same number of entries.
- A matrix with a zero determinant (singular) has no inverse.
- Decimal arithmetic: very small values (about 10⁻¹²) are rounded to 0.
When to use it
- Check linear algebra exercises and calculations.
- Find the determinant or inverse of a small matrix.
Frequently asked questions
What is this tool used for?
Type each matrix row by row: numbers in a row separated by spaces, rows by “;” or a new line.
How is the result calculated?
Sum and difference: entry by entry, both matrices must have the same size.
What should I check before using the result?
Maximum size 4 × 4. Every row must have the same number of entries.