Norm:

The definition of a scalar product implicitly defines a norm $\vert\vert\cdot\vert\vert$ that we can use to measure distances:

$$\mathcal{D}^2_{xy} = (\underline{\textbf{x}}-\underline{\text... ...line{\textbf{y}}-\underline{\textbf{y}}^h\underline{\textbf{x}}$$

Which respectively allows us to define the Power and Energy. For energy-type signals, the energy content of the signal is:

$$\mathcal{E}_{x} = <\underline{\textbf{x}},\underline{\textbf{x}}>$$

And for power-type signals the power content is:

$$\mathcal{P}_{x} = <\underline{\textbf{x}},\underline{\textbf{x}}>$$

For each one its respective definition of scalar product has to be used.