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I have the following matrix form $[J]$:

$$ \begin{bmatrix} \{ v[3],p + v[2]\}\\ \{v[3], p + v[2], 2 p + v[1]\} \\ \{v[3], p + v[2],2 p + v[1], 3 p + v[0]\}\\ \{v[3], p + v[2],2 p + v[1], 3 p + v[0]\} \\ \vdots \end{bmatrix} $$

I need to operate the list of each row by Max and Integrate and then add them all together like this:

$H=\int\limits_{0}^{\infty} \max \{ v[3],p + v[2]\}dF(p)+\int\limits_{0}^{\infty} \max \{v[3], p + v[2], 2 p + v[1]\}dF(p)+\dots$

I would like to use matrix operations to do it instead of loops, but I can't find a way to make it work.

Any help is appreciated. Thanks

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  • $\begingroup$ Do you know each v[i] values; Total[Integrate[Max[#], {p, 0, Infinity}] & /@ J] ? $\endgroup$ – Okkes Dulgerci Mar 25 '18 at 16:25
  • $\begingroup$ all except the last one, from H I will solve the last value v[3] $\endgroup$ – Rodrigo Mar 25 '18 at 16:29
  • $\begingroup$ I see. Can you post actual vector values if it is not too long. What is the length of J? $\endgroup$ – Okkes Dulgerci Mar 25 '18 at 16:34
  • $\begingroup$ I couldn't by pass the code formatting thing here is a link with a picture of J with n=10, at some point I would want to go for n=100 Matrix $\endgroup$ – Rodrigo Mar 25 '18 at 16:51
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The line of Okkes works, this do the job

Total[Integrate[Max[#], {p, 0, Infinity}] & /@ J]

Thanks!

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