Norm Properties
There are many other possible choices of norm. To qualify as a norm
on
, a realvalued
signalfunction
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).
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