The Norm command computes the p-norm of a.

If p is set to Euclidean, then the $2$-norm is computed.

For a real number p, the p-norm of a $n$-dimensional Vector v is given by ${\left(\sum _{i=1}^n{\left|v_i\right|}^p\right)}^{\frac{1}{p}}$.

The infinity norm of a $n$-dimensional Vector v is given by $\underset{i=1}{\overset{n}{\max }}\left|v_i\right|$.

Let $\left|\left|v\right|\right|$ denote the p-norm or infinity norm of a Vector v. The p-norm or infinity norm of a Matrix a is given by $\underset{\left|\right|v\left|\right|=1}{\max }\left|\right|a.v\left|\right|$.

Only the $1$, $2$, and infinity norms are available for Matrices.

$\mathrm{with}\left(\mathrm{Student}:-\mathrm{MultivariateCalculus}\right)\:$

$v≔⟨1\,2\,3⟩$

$v≔\left[\begin{array}{c}1\\ 2\\ 3\end{array}\right]$

$\mathrm{Norm}\left(v\right)$

$\sqrt{14}$

$\mathrm{Norm}\left(v\,\mathrm{\infty }\right)$

$3$

$\mathrm{Norm}\left(v\,1\right)$

$6$

$a≔⟨⟨1\,2⟩|⟨3\,4⟩⟩$

$a≔\left[\begin{array}{cc}1& 3\\ 2& 4\end{array}\right]$

$\mathrm{Norm}\left(a\right)$

$\sqrt{15+\sqrt{221}}$

$\mathrm{Norm}\left(a\,1\right)$

$7$

$\mathrm{Norm}\left(a\,\mathrm{\infty }\right)$

$6$

The Student[MultivariateCalculus][Norm] command was introduced in Maple 2016.

For more information on Maple 2016 changes, see Updates in Maple 2016.