Question: Problem with QR algorithm

I'm trying to implement the QR algorithm to find the Eigenvalues of the input matrix which will be forwarded to another implementation (of the SVD alg.) to find the singular values. My implementation goes as follows:

1. feeding input: A::Matrix(datatype=float) # a bidiagonal matrix
2. construct input matrix for the QR alg. of matrix A and Z (zeros of size A): C := Matrix([[Z,Transpose(A)],[A,Z]], datatype=float); # therefore C should be symmetric
3. find the eigenvalues of matrix C with an implementation of the QR alg.:

for k from 1 to 400 do
Q, R := QRDecomposition(C);
end do:

At this point, the eigenvalues of C should be placed in the diagonal of the matrix, but they're randomly placed around the diagonal, with only ~0 elements (like 2,xxx * 10^(-13)) in the diagonal.

If anyone knows how to resolve this, let the knowledge flow through. Any help will be appriciated, thanks in advance.

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