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Say I have a correlation matrix that measures how well certain components in a system track each other along some meaningful dimension, like condition state:

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So, for example, component 1 and component 2 have condition states that track 80% but component 1 and 3 are not related at all.

I want to perform some inspection on a subset of those, with the hope that I can gain some information about the larger system as a whole without inspecting everything.

In an ideal situation, I could inspect everything, where an inspection vector, [I], is 1 when a component is inspected [I] = [1, 1, 1, 1, 1] and the total information is 100%.

Assume I have an assigned cost to inspect each component; I'd like to set up an optimization problem to assign [I] with the goal to get as close as possible to 100% information within a budget constraint. I'm not sure if there's a way to logically set up matrix operations to do this.

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