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Mathematics
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Interesting Matrix Identity
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[QUOTE="madness, post: 6197710, member: 28629"] Thanks for the help. [USER=376845]@jedishrfu[/USER] I discovered this trying to maximise the following: [tex] \frac{\left[ \int_0^\infty f(t) dt \right]^2}{\int_0^\infty f^2(t) dt } [/tex] where [tex] f(t) = \sum_{i=1}^N w_i \frac{(ct)^{N-i}}{(N-i)!} e^{\lambda t} [/tex] and [tex] w_i [/tex] are weights which I want to maximise with respect to. I can show that the maximum is [tex] \frac{1}{-\lambda} \sum_{ij} \left(S^{-1}\right)_{ij} [/tex] and using Matlab this turns out to be [tex]\frac{2N}{-\lambda}[/tex] for N=1...15 (I stopped here as it became numerically unstable). [USER=511972]@TeethWhitener[/USER] I can see that your approach must give the right answer, but finding a closed form expression for the cofactor seems difficult for an arbitrary NxN matrix. [/QUOTE]
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