Statistical Methods
Identify which matrix norm a numerical report uses
Define the task
A numerical tolerance needs a scale and a norm definition. Preserve the row and column units before comparing matrix magnitudes. A norm aggregates entries into one nonnegative number, but different definitions emphasize different features. Record the selected convention in the analysis output so a later implementation can reproduce it.
Carry out the check
The matrix one-norm is the largest absolute column sum. The infinity norm is the largest absolute row sum. The Frobenius norm is the square root of the sum of squared entries. Use absolute values before summing so opposing signs do not cancel. Check a deliberately asymmetric matrix because row and column sums can coincide for a symmetric example.
Worked hypothetical example
For a hypothetical matrix with rows (1,2) and (3,4), the column sums are 4 and 6, the row sums are 3 and 7, and the squared entries sum to 30. Its one-norm is 6, infinity norm is 7 and Frobenius norm is approximately 5.4772. None of these alone proves numerical stability or justifies a common tolerance across differently scaled variables.
Method checked 12 November 2026 against R documentation: Compute the Norm of a Matrix.