# How to make sure each column in a matrix sums exactly to 1?

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Marco on 7 Aug 2015
Commented: Marco on 7 Aug 2015
Hello,
I would need to create a matrix of random numbers between 1 and 0, where the diagonal of the matrix is composed of zeros only and where each column sums to 1. I approximately reached the result by the following code, but some of the columns add up to slightly less than 1 (around 0.97). Why doesn't Matlab manage to normalize all of them to 1? Is there a way to solve the problem?
Here's the code:
a = [0:0.0001:1];
b(1:10000) = (0.5/10000);
F=randsrc(100,100,[a;0.5 b]);
columnSums = sum(F);
N=100;
for n=1:N
F(n,n)=0;
end
for i = 1:numel(columnSums)
F(:,i) = F(:,i)./columnSums(i);
end
Thank you! Marco

Lukas Bystricky on 7 Aug 2015
It's because you're calculating the column sums and then setting the diagonal entries to 0. If you calculate the sums after you modify the diagonal then what you wrote would work.
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Marco on 7 Aug 2015
Thank you!

### More Answers (1)

Torsten on 7 Aug 2015
a = [0:0.0001:1];
b(1:10000) = (0.5/10000);
F=randsrc(100,100,[a;0.5 b]);
N=100;
for n=1:N
F(n,n)=0;
end
columnSums = sum(F);
for i = 1:numel(columnSums)
F(:,i) = F(:,i)./columnSums(i);
end
Best wishes
Torsten.
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Marco on 7 Aug 2015
Thank you!