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Student[MultivariateCalculus]

 Norm

 Calling Sequence Norm(a, p)

Parameters

 a - Vector or Matrix with algebraic entries p - (optional) a real number greater than or equal to $1$, infinity, or Euclidean; defaults to $2$

Description

 • 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 $\underset{i=1}{\overset{n}{\mathrm{max}}}|{v}_{i}|$.
 • 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 $\underset{||v||=1}{\mathrm{max}}||a.v||$.
 • Only the $1$, $2$, and infinity norms are available for Matrices.

Examples

 > $\mathrm{with}\left(\mathrm{Student}:-\mathrm{MultivariateCalculus}\right):$
 > $v≔⟨1,2,3⟩$
 ${v}{≔}\left[\begin{array}{c}{1}\\ {2}\\ {3}\end{array}\right]$ (1)
 > $\mathrm{Norm}\left(v\right)$
 $\sqrt{{14}}$ (2)
 > $\mathrm{Norm}\left(v,\mathrm{∞}\right)$
 ${3}$ (3)
 > $\mathrm{Norm}\left(v,1\right)$
 ${6}$ (4)
 > $a≔⟨⟨1,2⟩|⟨3,4⟩⟩$
 ${a}{≔}\left[\begin{array}{cc}{1}& {3}\\ {2}& {4}\end{array}\right]$ (5)
 > $\mathrm{Norm}\left(a\right)$
 $\sqrt{{15}{+}\sqrt{{221}}}$ (6)
 > $\mathrm{Norm}\left(a,1\right)$
 ${7}$ (7)
 > $\mathrm{Norm}\left(a,\mathrm{∞}\right)$
 ${6}$ (8)

Compatibility

 • The Student[MultivariateCalculus][Norm] command was introduced in Maple 2016.
 • For more information on Maple 2016 changes, see Updates in Maple 2016.