Norm - Maple Help

Physics[Vectors][Norm] - calculate the norm of a vector

 Calling Sequence Norm(A) Norm(A, conjugate = ...)

Parameters

 A - any algebraic (vectorial or scalar) expression conjugate = ... - optional, can be the word conjugate alone, or the right-hand side can be true or false - by default it is equal to false unless you change the value of Physics:-Setup(normusesconjugate).

Description

 • If $A$ is a vector in the context of the Physics[Vectors] package, Norm returns its Euclidean norm, that is, $\sqrt{A·A}$ unless $A$ is not commutative or the option conjugate = true is passed, or the value of Physics:-Setup(normusesconjugate) is set to true - in all these cases it returns $\sqrt{{\left(A·\stackrel{&conjugate0;}{A}\right)}^{}}$. To expand the norm of a sum of unprojected vectors in terms of their dot product, use expand. In the case of a scalar, it respectively returns ${A}^{2}$ or the absolute value $\left|A\right|$ depending on the extra argument conjugate = ..., or the value of Physics:-Setup(normusesconjugate). Regarding how vector is identified in the context of the Physics[Vectors] package see Identify).
 • The %Norm is the inert form of Norm, that is, it represents the same mathematical operation while holding the operation unperformed. To activate the operation use value.

Examples

 > $\mathrm{with}\left(\mathrm{Physics}\left[\mathrm{Vectors}\right]\right)$
 $\left[{\mathrm{&x}}{,}{\mathrm{+}}{,}{\mathrm{.}}{,}{\mathrm{ChangeBasis}}{,}{\mathrm{ChangeCoordinates}}{,}{\mathrm{Component}}{,}{\mathrm{Curl}}{,}{\mathrm{DirectionalDiff}}{,}{\mathrm{Divergence}}{,}{\mathrm{Gradient}}{,}{\mathrm{Identify}}{,}{\mathrm{Laplacian}}{,}{\nabla }{,}{\mathrm{Norm}}{,}{\mathrm{Setup}}{,}{\mathrm{diff}}\right]$ (1)
 > $\mathrm{Setup}\left(\mathrm{mathematicalnotation}=\mathrm{true}\right)$
 $\left[{\mathrm{mathematicalnotation}}{=}{\mathrm{true}}\right]$ (2)
 > $a\mathrm{_i}+b\mathrm{_j}+c\mathrm{_k}$
 ${a}{}\stackrel{{\wedge }}{{i}}{+}{b}{}\stackrel{{\wedge }}{{j}}{+}{c}{}\stackrel{{\wedge }}{{k}}$ (3)
 > $\mathrm{Norm}\left(\right)$
 $\sqrt{{{a}}^{{2}}{+}{{b}}^{{2}}{+}{{c}}^{{2}}}$ (4)
 > $\mathrm{Norm}\left(,\mathrm{conjugate}\right)$
 $\sqrt{{a}{}\stackrel{{&conjugate0;}}{{a}}{+}{b}{}\stackrel{{&conjugate0;}}{{b}}{+}{c}{}\stackrel{{&conjugate0;}}{{c}}}$ (5)
 > $\mathrm{convert}\left(,\mathrm{abs}\right)$
 $\sqrt{{\left|{a}\right|}^{{2}}{+}{\left|{b}\right|}^{{2}}{+}{\left|{c}\right|}^{{2}}}$ (6)
 > $\mathrm{Norm}\left(\mathrm{A_}\right)$
 ${\mathrm{Norm}}{}\left({\mathrm{A_}}\right)$ (7)

For scalars, Norm returns their square, as in the Euclidean Norm, or the absolute value when the optional argument conjugate = true is passed, or the setting of normusesconjugate is set to true using Setup.

 > $\mathrm{Norm}\left(A\right)$
 ${{A}}^{{2}}$ (8)
 > $\mathrm{Norm}\left(A,\mathrm{conjugate}=\mathrm{true}\right)$
 $\left|{A}\right|$ (9)
 >