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RotationMatrix

RotationMatrix[]
gives the 2D rotation matrix that rotates 2D vectors counterclockwise by radians.
RotationMatrix[, w]
gives the 3D rotation matrix for a counterclockwise rotation around the 3D vector w.
RotationMatrix[{u, v}]
gives the matrix that rotates the vector u to the direction of the vector v in any dimension.
RotationMatrix[, {u, v}]
gives the matrix that rotates by theta radians in the hyperplane spanned by u and v.
  • RotationMatrix gives matrices for rotations of vectors around the origin.
  • Two different conventions for rotation matrices are in common use.
  • RotationMatrix is set up to use the vector-oriented convention and to give a matrix m so that m.r yields the rotated version of a vector r.
  • Transpose[RotationMatrix[...]] gives rotation matrices with the alternative coordinate-system-oriented convention for which r.m yields the rotated version of a vector r.
  • Positive in RotationMatrix[, {u, v}]corresponds to going from the direction of u towards the direction of v.
  • RotationMatrix gives an orthogonal matrix of determinant 1, that in n dimensions can be considered an element of the group SO (n).
New in 6