Understand the subject
What does a condition number measure?
A condition number estimates how much small input changes can be amplified by a matrix operation.
Use it to interpret numerical sensitivity, not to judge a model’s real-world quality.
See the structure
What the calculation is doing
input matrix→bounded numerical method→labelled approximation
Worked interpretation
Read the result in context
κ₂(A)=σmax/σmin
Interpret with care
Important boundary
A singular matrix has no finite condition number; near-singular conclusions depend on numerical tolerance.
Use the Matrix Calculator to experiment with small exact matrix operations before applying a more specialized route.
Quick guide
How to use this calculator
- Set the matrix dimensions required by the task.
- Fill every visible entry and any operation-specific control.
- Read the result type, factors, classification, and disclosed limitations.
Calculation method
Apply the stated linear-algebra contract
κ₂(A) = σmax/σmin
Undefined, singular, dimensionally incompatible, dependent, or unsupported inputs receive an explicit message instead of a fabricated numeric result.
Worked example
Example interpretation
A zero smallest singular value means the matrix is singular rather than a finite result.
κ₂(A) = σmax/σmin
Supported inputs
Precision and limits
Matrix size
Input matrices are limited to 1–6 rows and columns; operation-specific square, rank, or compatibility rules still apply.
Entry precision
Enter signed finite decimals with at most 30 digits and 15 decimal places.
Numerical policy
Results use real double-precision arithmetic, a 1e-10 structural tolerance where stated, bounded iterations, and labelled approximations.
