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A matrix's condition number measures how sensitive solutions to Ax=b are to small errors in A or b — a large condition number means tiny input changes can cause wildly different outputs. This tool computes it via the same singular value decomposition used by the SVD calculator.
How it works
The matrix's singular values are found through SVD (via Jacobi rotations on AᵀA), and the condition number is simply the largest singular value divided by the smallest.
- Click Calculate to see your results.
Examples
A well-conditioned matrix
The identity matrix has all singular values equal to 1, giving a condition number of exactly 1 — the best possible case.
An ill-conditioned matrix
A matrix with singular values 100 and 0.01 has a condition number of 10,000 — small input errors could be amplified enormously.
Who should use it
- Numerical linear algebra and scientific computing coursework.
- Checking whether a matrix is safe to invert numerically before relying on the result.
Industry applications
- Numerical analysis
- Engineering simulation and scientific computing
Advantages
- Reuses the same verified SVD engine as the site's SVD calculator.
- Explicitly flags singular (infinite condition number) matrices.
Limitations
- Limited to square matrices up to 6x6.
Common mistakes to avoid
- Assuming a large determinant means a matrix is well-conditioned — determinant size and condition number are not directly related.
Best practices
- Treat a condition number above roughly 100-1000 as a signal that numerical solutions (e.g. from Gaussian elimination) may lose significant precision.
Tips
- If you're solving Ax=b and get suspiciously different answers from small changes in b, check A's condition number first — it's often the culprit.