SpaceTest.norm

SpaceTest.norm(self)

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.