SpaceTest.norm

SpaceTest.norm(self)[source]

Verify LinearSpace.norm.

The norm is checked for the following properties:

  • linearity:

    ||a * x|| = |a| * ||x||

  • subadditivity:

    ||x + y|| <= ||x|| + ||y||

  • positive homogeneity:

    ||a * x|| = |a| * ||x||

  • positive definiteness:

    ||x|| >= 0

    ||x|| = 0 iff x = 0

  • compatibility with the inner product (if available):

    ||x||^2 = <x, x>

References

Wikipedia article on norm.