Definition:P-Norm

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Definition

Let $p \ge 1$ be a real number.

Let $\ell^p$ denote the $p$-sequence space.

Let $\mathbf x = \sequence {x_n} \in \ell^p$.


Then the $p$-norm of $\mathbf x$ is defined as:

$\ds \norm {\mathbf x}_p = \paren {\sum_{n \mathop = 0}^\infty \size {x_n}^p}^{1/p}$


Also see

  • Results about $p$-norms can be found here.





Sources