Logarithm of a matrix: Difference between revisions

Revision as of 19:16, 21 October 2021

Revision as of 19:22, 21 October 2021

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A rotation {{mvar|R}} ∈ SO(3) in ℝ³ 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]]<ref>Engø, (2001)</ref>explicitly (seein also [[Axis–angle representation#Log map from SO.283.29 to so.283.29|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'',