Rotation Matrix - Examples

Examples

  • The 2×2 rotation matrix
    corresponds to a 90° planar rotation.
  • The transpose of the 2×2 matrix
    is its inverse, but since its determinant is −1 this is not a rotation matrix; it is a reflection across the line 11y = 2x.
  • The 3×3 rotation matrix
    corresponds to a −30° rotation around the x axis in three-dimensional space.
  • The 3×3 rotation matrix
    corresponds to a rotation of approximately -74° around the axis (−1⁄3,2⁄3,2⁄3) in three-dimensional space.
  • The 3×3 permutation matrix
    is a rotation matrix, as is the matrix of any even permutation, and rotates through 120° about the axis x = y = z.
  • The 3×3 matrix
    has determinant +1, but its transpose is not its inverse, so it is not a rotation matrix.
  • The 4×3 matrix
    is not square, and so cannot be a rotation matrix; yet MTM yields a 3×3 identity matrix (the columns are orthonormal).
  • The 4×4 matrix
    describes an isoclinic rotation, a rotation through equal angles (180°) through two orthogonal planes.
  • The 5×5 rotation matrix
    rotates vectors in the plane of the first two coordinate axes 90°, rotates vectors in the plane of the next two axes 180°, and leaves the last coordinate axis unmoved.

Read more about this topic:  Rotation Matrix

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