ReflectionMatrix
Creates a reflection matrix.
Syntax
-
ReflectionMatrix(v)
-
v
is a vector
-
Description
If v
is a non-zero vector, then ReflectionMatrix(v)
returns the matrix for reflection in the hyperplane having v
as a normal.
If w ≔ normalized(v)
then
ReflectionMatrix(v) = IdentityMatrix(dim(v)) − 2⋅w⊗w
Examples
A ≔ ReflectionMatrix(❨1, 3, −2❩)
⎛ 0.857142857143 −0.428571428571 0.285714285714⎞ ⎜−0.428571428571 −0.285714285714 0.857142857143⎟ ⎝ 0.285714285714 0.857142857143 0.428571428571⎠
IsSymmetric(A) ∧ IsOrthogonal(A) ∧ IsInvolution(A) ∧ spectrum(A) = {−1, 1} ∧ det(A) = −1
true