Norm Induced by the Inner Product

GUIDE: Mathematics of the Discrete Fourier Transform (DFT). Norm Induced by the Inner Product

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Norm Induced by the Inner Product

We may define a norm on $\ using the inner product:

\

It is straightforward to show that properties 1 and 3 of a norm hold. Property 2 follows easily from the Schwarz Inequality which is derived in the following subsection. Alternatively, we can simply observe that the inner product induces the well known $L_2$ norm on ${\.

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