Vector Norm

For a vector $\mathbf{z}$, the ${\ell }_p$ norm is defined as:

$$||\mathbf{z}|{|}_p={\left(\sum _{d=1}^D{\left|z_d\right|}^p\right)}^{1/p}$$

for real-valued $p\ge 1$.

• When $p=2$, this returns the length of the vector, and this is known as the Euclidean norm.
• When $p=\infty$, the operator returns the maximum absolute value in the vector (infinity norm)