There are many other possible choices of norm. To qualify as a norm
on , a real-valued signal-function
must
satisfy the following three properties:

, with

,

The first property, ``positivity,'' says the norm is nonnegative, and
only the zero vector has norm zero. The second property is
``subadditivity'' and is sometimes called the ``triangle inequality''
for reasons that can be seen by studying
Fig.5.6. The third property says the norm is
``absolutely homogeneous'' with respect to scalar multiplication. (The
scalar can be complex, in which case the angle of has no effect).