RotationMatrix

Creates a rotation matrix.

Syntax

• RotationMatrix(θ, v)

  • θ is a real number

  • v is a three-dimensional vector

• RotationMatrix(θ[, n[, i, j]])

  • θ is a real number

  • n is a positive integer

  • i and j are distinct positive integers in [1, n]

Description

If θ is a real number and v a vector in ℝ³, then RotationMatrix(θ, v) returns the matrix for a rotation θ radians about v.

If θ is a real number, n a positive integer, and i and j are distinct integers between 1 and n, then RotationMatrix(θ, n, i, j) returns the matrix for a rotation θ radians in the ij plane of ℝⁿ. If omitted, n defaults to 2 and (i, j) to (1, 2).

Examples

RotationMatrix(π/6, ❨1, 3, −1❩)

⎛ 0.878204912531   0.187294198529    0.44008750812⎞
⎜−0.114217146048   0.975640982506  −0.187294198529⎟
⎝−0.464446525614   0.114217146048   0.878204912531⎠

RotationMatrix(π/6, 4, 3, 4)

⎛             1               0               0               0⎞
⎜             0               1               0               0⎟
⎜             0               0  0.866025403784            −0.5⎟
⎝             0               0             0.5  0.866025403784⎠

See also

• ReflectionMatrix