A paper I'm reading states the that: for positive hermitian matrices A and B, the Taylor expansion of [itex]\log(A+tB)[/itex] at t=0 is(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\log(A+tB)=\log(A) + t\int_0^\infty \frac{1}{B+zI}A \frac{1}{B+zI} dz + \mathcal{O}(t^2).[/itex]

However, there is no source or proof given, and I cannot seem to find a derivation of this identity anywhere! Any help would be appreciated. Thanks.

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# Taylor expansion for matrix logarithm

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