### Other Lp Norms

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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