Since our main
norm is the square root of a sum of squares,

we are using what is called an
norm and we may write

to emphasize this fact.
We could equally well have chosen a
normalized
norm:
which is simply the ``RMS level'' of

(``Root Mean Square'').
More generally, the (unnormalized)
norm of

is defined as
(The normalized case would include

in front of the summation.)
The most interesting

norms are
: The
, ``absolute value,'' or ``city block'' norm.
: The
, ``Euclidean,'' ``root energy,'' or ``least squares'' norm.
: The
, ``Chebyshev,'' ``supremum,'' ``minimax,''
or ``uniform'' norm.
Note that the case

is a limiting case which becomes
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