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en.wikipedia.org/wiki/Logarithm_of_a_matrix#Existence mentions it always exists for all invertible complex matrices. But the real condition is more complicated. Notable counter example: -1 cannot be reached by any real .
The Lie algebra exponential covering problem can be seen as a generalized version of this problem, because
  • Lie algebra of is just the entire
  • we can immediately exclude non-invertible matrices from being the result of the exponential, because has inverse , so we already know that non-invertible matrices are not reachable

Ancestors

  1. Logarithm of a matrix
  2. Matrix exponential
  3. Exponential function
  4. Exponentiation
  5. Numeric function
  6. Function by signature
  7. Function
  8. Formalization of mathematics
  9. Area of mathematics
  10. Mathematics
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Synonyms