How this calculation works
Measure a real matrix by treating its entries as one vector.
THE FORMULA
‖A‖F = √Σ |aᵢⱼ|²A worked example
The entries 1, −2, 3 and 4 contribute squares 1+4+9+16.
Good to know
This is an entrywise norm and differs from the largest singular value.
Reference: OpenStax Algebra and Trigonometry (opens in a new tab) ↗
Read the result
Measure a real matrix by treating its entries as one vector.
The primary result is labeled “Frobenius norm”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
This is an entrywise norm and differs from the largest singular value.
For a related exercise, try the quadratic equation solver.
A few questions, answered
How can I check the default inputs by hand?
The entries 1, −2, 3 and 4 contribute squares 1+4+9+16.
Which rule does this calculator apply?
‖A‖F = √Σ |aᵢⱼ|²