That such a rotation exists corresponds precisely to a main result of the mathematical theory of rotation operators, the ( only real ) eigenvector of the rotation operator corresponding to the desired re-orientation is this axis.
12.
That such a rotation exists corresponds precisely to a main result of the mathematical theory of rotation operators, the ( only real ) eigenvector of the rotation operator corresponding to the desired re-orientation is this axis.
13.
Given the current orientation of the craft, and the desired orientation of the craft in cartesian coordinates, the required axis of rotation and corresponding rotation angle to achieve the new orientation is determined by computing the eigenvector of the rotation operator.
14.
Again, a finite rotation can be made from lots of small rotations, replacing ? " ? " by and taking the limit as " N " tends to infinity gives the rotation operator for a finite rotation.
15.
Because this is the matrix of the rotation operator relative the base vector system \ hat { a } \, \ \ hat { b } \, \ \ hat { c } the eigenvalue can be determined with the algorithm described in " Rotation operator ( vector space ) ".
16.
Because this is the matrix of the rotation operator relative the base vector system \ hat { a } \, \ \ hat { b } \, \ \ hat { c } the eigenvalue can be determined with the algorithm described in " Rotation operator ( vector space ) ".
17.
Because the exchange of two identical particles is mathematically equivalent to the rotation of each particle by 180 degrees ( and so to the rotation of one particle's frame by 360 degrees ), the symmetric nature of the wave function depends on the particle's rotation operator is applied to it.
