calculate the norm of a vector - Maple Help

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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, 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 A . A&conjugate0;. 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 A2 or the absolute value A 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

withPhysics[Vectors]

&x,`+`,`.`,ChangeBasis,ChangeCoordinates,Component,Curl,DirectionalDiff,Divergence,Gradient,Identify,Laplacian,Nabla,Norm,Setup,diff

(1)

Setupmathematicalnotation=true

mathematicalnotation=true

(2)

a_i+b_j+c_k

ai+bj+ck

(3)

Norm

a2+b2+c2

(4)

Norm,conjugate

aa&conjugate0;+bb&conjugate0;+cc&conjugate0;

(5)

convert,abs

a2+b2+c2

(6)

NormA_

A

(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.

NormA

A2

(8)

NormA,conjugate=true

A

(9)

See Also

Identify, operations, Physics, Physics conventions, Physics examples, Physics[Vectors], Setup


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