I am not really a math guy, I had no clue what to title this question...
Anyways, the question:
I have a collection of values, let's say it's form is a matrix. When I select a value from this matrix, I can no longer select a value from that row or column.
I want to select minimal values from the matrix. This means that I want to avoid picking values, even if they are small, if they take away other small values I could potentially pick.
So my question is, is there a way to transform all of the values in my matrix, such that the values that are closer to zero (the smaller values) become larger, and in turn the values that are larger become smaller, while still maintaining some kind of proportionality to my original matrix?
Example:
[[2, 4, 7], [3, 11, 1], [5, 6,8]]
So I can pick say:
2,11,8
or 2,1,6 or 4,3,8 etc
And so, any pick I make can not only be measured in terms of it's own magnitude, but also in terms of the magnitude of the rest of the row and column. Since it is required that for each pick, I will remove several other picks - then if that magnitude is greater it suggests the pick may be better.
But to take this one step further, what is specifically more important is that I do not pick entries that remove other good picks.
And, I feel that I could get a strong indicator for if I am going to remove other good picks, if I could make the small numbers stand out. Simply taking the sum is not good enough. It could be the case that all of my alternatives are "average" in magnitude, and there would be no way to tell the difference between this situation, and a situation where I was removing 2 optimal choices and some very poor choices. So, I need a way to make my choices stand out more and more as their magnitude is lower, and less and less as their magnitude is higher.
Hopefully someone is following what I am asking for....