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The matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function.

9 votes

Logarithm of a bounded operator

The other answer is not correct. If $L$ is the half-line issuing from the origin, then we can find a branch of the logarithm that is holomorphic on $\mathbb{C}\setminus L \supset{\rm spec}(A)$. Then a …
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