# Adding mirror image of lower triangle of matrix to upper half of matrix

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Samuel on 10 Oct 2011
Hello all!
I just had a question about combining elements of matrices. In the matlab documentation, there was a function called triu and tril that extracts the upper and lower components of a matrix, respectively. I was wondering if there was a way to copy the elements of the upper triangle to the lower triangle portion of the symmetric matrix (or visa versa) as a mirror image to one another?
EG-
haha =
1 0 0 ;
1 1 0;
1 0 1 ;->
function (copy lower half to upper half)(haha)
1 1 1;
1 1 0;
1 0 1;
any help will be appreciated. thanks!
UPDATE- I found an article from a website that wrote the method below, but I can't entirely understand it, and moreover, don't know how I can apply this for the lower matrix, copying to the upper half. I was hoping to be able to understand the code to be able to convert, but I can't understand the code.. and testing the code gives me a mupadmex error.
here it is:
[ i j ] = find(tril(ones(m), 1)); %Trick to get indices.
D = zeros(m, m); %Initialise output matrix.
D( i + m*(j-1) )= sqrt(sum(abs( kmat(i,:) - kmat(j,:) ).^2, 2));
D( j + m*(i-1) )= D( i + m*(j-1) );
When I actually try to go through the operation to build the first half triangle of the matrix (in order to copy it to the upper half), it gives me a CAT error, saying that a matrix cannot contain components that are empty. Is there a way to build a half-matrix so I can go through this entire operation without having to manually pad the other half of the matrix with zeros?
Thanks!
samuel

Andrei Bobrov on 10 Oct 2011
tril(haha,-1)'+haha
h1 =[ 1 1 0 1 0
0 0 1 0 1
0 1 0 1 0
0 0 0 0 0
0 0 0 1 0]
triu(h1)+triu(h1,1)' % upper matrix, copyed to the lower half
tril(h1)+tril(h1,-1)' % lower matrix, copyed to the upper half

Walter Roberson on 10 Oct 2011
The only way to build a "half-matrix" is to use cell arrays, which are usually a nuisance for this kind of work.
Here is a trick for square matrices, provided that only half the matrix (together with the diagonal) are occupied:
B = haha + haha.';
B(1:size(B,1)+1:end) = diag(haha);

Quincy van den Berg on 27 Mar 2012
The trick mentioned above seems to work, adding the transpose to your original matrix. It does however double the diagonal so it needs to be removed.
Suppose you have a matrix H that you want to mirror the upper half of:
H=H+H'-diag([diag(H)]);