Let $$A,B:V\to V$$ positive definite operators in complex linear space with inner product $$V$$, $$dimV<\infty$$ Show that $$log det(A\cdot B^{-1})=-\int_{0}^\infty tr(e^{-t\cdot A}-e^{-t\cdot B}){dt\over t}$$
Can anyone help me and give me a proof?
2026-03-28 02:43:02.1774665782
Let $A,B:V\to V$ positive definite operators in complex linear space with inner product $V$, $dimV<\infty$
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