Logarithm of a matrix: Difference between revisions

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A rotation {{mvar|R}} ∈ SO(3) in <math>\mathbb{R}</math>³ is given by a 3×3 [[orthogonal matrix]].

The logarithm of such a rotation matrix {{mvar|R}} can be readily computed from the antisymmetric part of [[Rodrigues' rotation formula]], explicitly in [[Axis–angle representationAxis-angle_representation#Log map from SO.283.29 to so.283.29Log_map_from_SO(3)_to_%F0%9D%94%B0%F0%9D%94%AC(3)|Axis angle]]. It yields the logarithm of minimal [[Frobenius norm]], but fails when {{mvar|R}} has eigenvalues equal to &minus;1 where this is not unique.

Further note that, given rotation matrices ''A'' and ''B'',