Condition Number Calculator (2×2)
The Condition Number Calculator measures how sensitive a 2×2 linear system is to input errors, using the infinity-norm condition number. Enter the four matrix entries.
Formula
cond(A) = ‖A‖∞ · ‖A⁻¹‖∞ (∞-norm = max absolute row sum)
- A condition number near 1 means the system is well-behaved.
- A large condition number means small input changes can cause large output errors.
[[2,1],[1,2]]
Inputs
- a₁₁: 2
- a₁₂: 1
- a₂₁: 1
- a₂₂: 2
‖A‖∞ = 3 and ‖A⁻¹‖∞ = 1, so the condition number is 3 (well-conditioned).
Frequently asked questions
What does the condition number tell you?
How much errors in the input can be amplified in the solution. Larger values mean less numerical stability.