Symbol meaning

Absolute Value vs Norm: |x| and ||x||

Compare single bars for scalar absolute value with double bars for vector, matrix, or function norms.

Compare the possible meanings

NotationTypical meaningHow to identify it
|x|Absolute valueScalar real or complex number
||v||₂Euclidean normVector
||A||Matrix normMatrix; definition must be stated
||f||pFunction normFunction 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.

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