Condition Number Calculator

The condition number of a matrix measures how sensitive the output of a function is to small changes in the input. A low condition number indicates a well-conditioned matrix, while a high condition number indicates an ill-conditioned matrix.

Formula:

The condition number of a matrix A is calculated as: cond(A) = ||A|| * ||A⁻¹||

• ||A|| is the norm of the matrix A. This calculator uses the infinity norm (maximum absolute row sum).
• A⁻¹ is the inverse of the matrix A.
• ||A⁻¹|| is the norm of the inverse matrix.

A matrix must be invertible (i.e., its determinant must not be zero) to have a condition number.