How this calculation works
Measure how far the columns are from being unit length and perpendicular.
THE FORMULA
‖AᵀA−I‖FA worked example
The matrix [[0,−1],[1,0]] rotates vectors by 90° and has residual zero.
Good to know
A small nonzero residual may be due to rounded entries.
Reference: OpenStax Algebra and Trigonometry (opens in a new tab) ↗
Read the result
Measure how far the columns are from being unit length and perpendicular.
The primary result is labeled “Frobenius residual”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
A small nonzero residual may be due to rounded entries.
For a related exercise, try the quadratic equation solver.
A few questions, answered
How can I check the default inputs by hand?
The matrix [[0,−1],[1,0]] rotates vectors by 90° and has residual zero.
Which rule does this calculator apply?
‖AᵀA−I‖F