# Random matrices with constraint

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Tato Khundadze on 12 Oct 2021
How to create random matrix with n=100, uniform distribution and with following constraints: 0<aij<1 and sum of columns less than 1. I have codes but they work only for small matricies.
DGM on 12 Oct 2021
If I get this right, you have a 100x100 array of uniformly distributed random numbers between 0,1 ... but the column sums are less than 1.
How do you have a uniform distribution on the interval [0 1] such that the mean is 1/100?

Walter Roberson on 12 Oct 2021
t = rand(n, n);
nt = t./sum(t,1);
output = nt.*rand(1,n);
nt is normalized so that the sum of each column is 1. The step after that is to scale to a random sum less than 1. You might want to use a different distribution in that scaling.

Tato Khundadze on 12 Oct 2021
Thanks, you are right. Uniform distribution will not work without scaling. I should consider the maybe Poisson distribution, which would assign lower marginal probabilities to the numbers which are closer to 1.