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BUILT-IN MATHEMATICA SYMBOL
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 radians in the hyperplane spanned by u and v.
Details
- 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
yields the rotated version of a vector r. - Transpose[RotationMatrix[...]] gives rotation matrices with the alternative coordinate-system-oriented convention for which
yields the rotated version of a vector r. - Angles in RotationMatrix are in radians. Degree 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[] is equivalent to RotationMatrix[, {{1, 0}, {0, 1}}].
- RotationMatrix[, w] is equivalent to RotationMatrix[, {u, v}], where
, 
, and 
form a right-handed coordinate system. - RotationMatrix gives an orthogonal matrix of determinant 1, that in
dimensions can be considered an element of the group 
.
Examplesopen all
Basic Examples (4)
General 2D rotation matrix for rotating a vector about the origin:
| In[1]:= |
Out[1]//MatrixForm= | |
 | |
Apply rotation by 
to a unit vector in the 
direction:
| In[2]:= |
| Out[2]= |  |
Counterclockwise rotation by 30°:
| In[1]:= |
| Out[1]= |  |
Rotation that transforms the direction of 
into the direction of 
:
| In[1]:= |
| Out[1]= |  |
| In[1]:= |
Out[1]//MatrixForm= | |
 | |
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