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determinant_differentiation [2016/07/18 23:14] nikolaj |
determinant_differentiation [2016/07/18 23:15] nikolaj |
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| This comes from [[http://en.wikipedia.org/wiki/Jacobi%27s_formula|Jacobi's formula]]: | This comes from [[http://en.wikipedia.org/wiki/Jacobi%27s_formula|Jacobi's formula]]: | ||
| - | $\mathrm{det}(F(t))^{-1}{\mathrm d} \det (F(t)) = \mathrm{tr} (F(t)^{-1} {\mathrm d}F(t))$ | + | ${\mathrm d} \log\left(\det (F(t))\right) = \mathrm{tr} (F(t)^{-1} {\mathrm d}F(t))$ |
| where $F(t)$ is a parameter dependent matrix | where $F(t)$ is a parameter dependent matrix | ||
