A Lie Group Theory Perspective
In the theory of Lie groups, there is an exponential map from a Lie algebra g to the corresponding Lie group G
For matrix Lie groups, the elements of g and G are square matrices and the exponential map is given by the matrix exponential. The inverse map is multivalued and coincides with the matrix logarithm discussed here. The logarithm maps from the Lie group G into the Lie algebra g. Note that the exponential map is a local diffeomorphism between a neighborhood U of the zero matrix and a neighborhood V of the identity matrix . Thus the (matrix) logarithm is well-defined as a map
Read more about this topic: Logarithm Of A Matrix
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