I am enquiring as to how the "Eigenvectors" function in Maple (I am using version 10) orders the eigenvalues that it returns (and hence the eigenvectors). That is to say, if I input it with a matrix of complex floats, does it just return the eigenvalues it happens to find randomly, or is there some ordering in the vector of eigenvalues it returns?
I ask this because if I input it with say a diagonal matrix that is symmetric about it's centre, then the vector of eignevalues returned is also symmetric. Is this just a coincidence in that maple happens to find the eigenvalues in that order, or does it choose to return them in that order? Otherwise, if there is no symmetry in the input matrix then there appears to be no symmetry in the returned vector of eigenvalues.
Thank you very much,