Condition Number Calculator

Compute the condition number kappa(A) = norm(A) times norm(A inverse) for a 2x2 or 3x3 matrix - measures how sensitive the system Ax = b is to small changes in inputs.

Frequently Asked Questions

What is a matrix condition number?

How much the relative error in the solution of Ax = b can be amplified by the relative error in A or b. Small kappa is good; large kappa is bad.

Frobenius versus 2-norm condition number?

The 2-norm condition number is the ratio of the largest to smallest singular value and is the standard. Frobenius is easier to compute and bounds the 2-norm within square root of n.

When is a system ill-conditioned?

When the condition number is very large (rule of thumb: greater than 10 to the 6 in double precision). Tiny input perturbations can produce huge changes in the solution.

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Estimates for informational purposes only.

Important Disclaimer: Estimates for informational purposes only.

This calculator provides estimates for informational purposes only. Results are based on assumptions and may not reflect actual outcomes. Consult qualified professionals in relevant fields before making important decisions based on these results.

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