This is documentation for Mathematica 6, which was
based on an earlier version of the Wolfram Language.

# 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 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.
• Angles in RotationMatrix are in radians. or ° specifies an angle in degrees.
• 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 .
General 2D rotation matrix for rotating a vector about the origin:
 Out[1]//MatrixForm=
Apply rotation by to a unit vector in the direction:
 Out[2]=

Counterclockwise rotation by 30°:
 Out[1]=

Rotation that transforms the direction of into the direction of :
 Out[1]=

3D rotation around the z axis:
 Out[1]//MatrixForm=
 Scope   (5)
 Applications   (2)
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