construct a reflection Matrix - Maple Help

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Student[LinearAlgebra][ReflectionMatrix] - construct a reflection Matrix

Calling Sequence

ReflectionMatrix(v)

Parameters

v

-

Vector; normal to the reflection subspace

Description

• 

The ReflectionMatrix(v) command returns the mxm reflection Matrix, R, determined by the Vector v, where m=Dimensionv. Thus R.v=v and R.w=w for all w such that v.w=0.

• 

In two-dimensional space, the reflection subspace is a line through the origin.  If the equation of this line is y=mx, or mxy=0, then v=m,1.

  

In three-dimensional space, the reflection subspace is a plane through the origin.

Examples

withStudent[LinearAlgebra]:

Reflect through the line y=-x:

ReflectionMatrix1,1

0110

(1)

ReflectionMatrixa,b,c

a2+b2+c2a2+b2+c22aba2+b2+c22aca2+b2+c22aba2+b2+c2a2b2+c2a2+b2+c22bca2+b2+c22aca2+b2+c22bca2+b2+c2a2+b2c2a2+b2+c2

(2)

ReflectionMatrix1,2,3,4

1415215154152151115258151525254541581545115

(3)

See Also

Student[LinearAlgebra], Student[LinearAlgebra][RotationMatrix]


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