Dear Statalisters:
I hope you are doing well.
I am trying to calculate the weakest link from a sample matrix (see matrix below). The weakest link assigns the control of the relationship between firms the controlling owner considering the minimum value of the voting rights across different links in a control chain.
In the sample below, the individual I owns 60% of shares in firm E that owns 50% of shares of firm B that owns 40% of shares of firm A, so that the control position of individual I in firm A, by the weakest link is 40%.
How to calculate that using the matrix?
The expected outcome is the controlling position of each owner in the chain of ownership in firm A, using as the "weakest link" as criteria.

Code:
* Example generated by -dataex-. To install: ssc install dataex
clear
input str1 id float(A B C D E F G I J)
"A" 0 .4 .4 .2  0  0 0  0  0
"B" 0  0  0  0 .5 .5 0  0  0
"C" 0  0  0  0  0  0 0  0  0
"D" 0  0  0  0  0  0 0  0  0
"E" 0  0  0  0  0  0 0 .6 .4
"F" 0  0  0  0  0  0 1  0  0
"G" 0  0  0  0  0  0 0 .6 .4
"I" 0  0  0  0  0  0 0  0  0
"J" 0  0  0  0  0  0 0  0  0
end
Thank you and warm regards.
LR