How this calculation works
Estimate the sensitivity of a linear system using the induced one-norm.
THE FORMULA
κ₁(A) = ‖A‖₁‖A⁻¹‖₁A worked example
For diagonal entries 2 and 0.5, both the matrix and its inverse have one-norm 2.
Good to know
A singular matrix has infinite condition number.
Reference: OpenStax Algebra and Trigonometry (opens in a new tab) ↗
Read the result
Estimate the sensitivity of a linear system using the induced one-norm.
The primary result is labeled “Condition number”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
A singular matrix has infinite condition number.
For a related exercise, try the quadratic equation solver.
A few questions, answered
How can I check the default inputs by hand?
For diagonal entries 2 and 0.5, both the matrix and its inverse have one-norm 2.
Which rule does this calculator apply?
κ₁(A) = ‖A‖₁‖A⁻¹‖₁