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  "body": "\n## Summary\n\nA logarithm of a square matrix $A$ is a matrix $B$ whose [[matrix exponential|020M04FN1H]] is $A$.\nOver the complex numbers, a matrix has a logarithm exactly when it is [[invertible|0EB9N0S33C]].\nThe logarithm is not unique, just as for the [[complex logarithm|02QGGD5G87]].\nMatrix logarithms pass from a matrix Lie group to its Lie algebra.\nThey are also used to interpolate between rotations and to find the generator of a linear system from its flow.\n\n## Explanations\n\n### L1 human\n\nFor numbers, the logarithm undoes the exponential.\nFor matrices, a logarithm of $A$ is any matrix $B$ with $e^B = A$.\nThe rotation of the plane by an angle $\\theta$ has the logarithm $\\begin{pmatrix} 0 \u0026 -\\theta \\\\ \\theta \u0026 0 \\end{pmatrix}$, an infinitesimal rotation.\nAdding $2\\pi$ to $\\theta$ gives the same rotation and another logarithm, so a logarithm is not unique.\n",
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