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{{Use American English|date = March 2019}}
{{Short description|Mathematical operation on invertible matrices}}
In [[mathematics]], a '''logarithm of a matrix''' is another [[matrix (mathematics)|matrix]] such that the [[matrix exponential]] of the latter matrix equals the original matrix. It is thus a generalization of the scalar [[logarithm]] and in some sense an [[inverse function]] of the [[matrix exponential]]. Not all matrices have a logarithm and those matrices that do have a logarithm may have more than one logarithm. The study of logarithms of matrices leads to [[Lie theory]] since when a matrix has a logarithm then it is in an element of a [[Lie group]] and the logarithm is the corresponding element of the vector space of the [[Lie algebra]].
==Definition==
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