Compare the possible meanings
| Notation | Typical meaning | How to identify it |
|---|---|---|
|x| | Absolute value | Scalar real or complex number |
||v||₂ | Euclidean norm | Vector |
||A|| | Matrix norm | Matrix; definition must be stated |
||f||p | Function norm | Function space |
Examples
- |−5|=5.
- ||(3,4)||₂=5.
- Different matrix norms can give different values for the same matrix.
How to decide
Use single bars for a scalar magnitude and double bars when a named norm is applied to a structured object.
How to verify the interpretation
Check that the result is nonnegative and that the chosen norm satisfies the definition used in the document.