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The matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function.
6
votes
How to prove this determinant is positive?
The conjecture ist true :
It follows from $$det(I + e^{M}) = det(I + i e^{M/2}) * det(I - i e^{M/2}) = {\left\lvert{det(I + i e^{M/2})}\right\lvert}^2 \ge 0$$ .
I.e. it follows from the fact that ev …