Every proper rotation A in 3D space has an axis of rotation, which is defined such that any vector v that is aligned with the rotation axis will not be affected by rotation. Accordingly, A v = v , and the rotation axis therefore corresponds to an eigenvector of the rotation matrix associated with an eigenvalue of 1. As long as the rotation angle α α is nonzero (i.e., the rotation is not the identity tensor), there is one and only one such direction. Because A has only real components, there is at least one real eigenvalue, and the remaining two eigenvalues must be complex conjugates of each other (see Eigenvalues and eigenvectors#Eigenvalues and the characteristic polynomial). Knowing that 1 is an eigenvalue, it follows that the remaining two eigenvalues are complex conjugates of each other, but this does not imply that they are complex—they could be real with double multiplicity. In the degenerate case of a rotation angle α α = 180 ∘ ∘ , the remaining two eigenvalues are both equal to −1. In the degenerate case of a zero rotation angle, the rotation matrix is the identity, and all three eigenvalues are 1 (which is the only case for which the rotation axis is arbitrary).