The Multiplicative Group
Behind the use of the logarithmic derivative lie two basic facts about GL1, that is, the multiplicative group of real numbers or other field. The differential operator
is invariant under 'translation' (replacing X by aX for a constant). And the differential form
- dX/X
is likewise invariant. For functions F into GL1, the formula
- dF/F
is therefore a pullback of the invariant form.
Read more about this topic: Logarithmic Derivative
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