If all of your matrices are the same size, it is trivial to store them, extracting the upper triangle.
Just create one vector. It will be a boolean vector, so cheap to store. For example, given a large upper triangular matrix...
clear
N = 5000;
UT = triu(rand(N,N)); % Our sample test matrix
% Now, create a boolean vector.
Boolind = triu(repmat(true,N,N));
Boolind = Boolind(:);
UTvec = UT(Boolind);
whos
Name Size Bytes Class Attributes
Boolind 25000000x1 25000000 logical
N 1x1 8 double
UT 5000x5000 200000000 double
UTvec 12502500x1 100020000 double
As you can see, UTvec is roughly half the size.
You can save UTvec as a vector now. If you have several matrices, no problem. Just save them all as vectors. You can also save the boolean vector, so it need not be recreated each time. But since it is of class logical, it is relatively small potatoes.
Now, can I recreate a new full matrix that is upper triangular and contains that upper triangle?
UTcopy = zeros(N);
UTcopy(Boolind) = UTvec;
max(max(abs(UT - UTcopy)))
ans =
0
It will take some small amount of time to stuff the data into a new array. But if you need to work with it as an array, you do what you need.
If you are creating several such arrays in turn, you can even save the time for the zeros allocation, just overwrite that upper triangle as I did in a simple assignment.
One other point. I don't know what you are doing with the arrays, since you have given us no clue at all. But suppose you wanted to just add two such arrays, when stored in vector form? Just add the vectors! As long as you will do only element-wise operations on only those elements, you can do it in purely vector form. So there might be many things you can do without ever needing to create an upper triangular matrix at all.
