Any subrout to compute the orthogonal complement?

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Any subrout in Lapack or IMSL or free code to compute the orthogonal complement of m vectors?

Now, there are m (m<n) vectors in a n-dimensional cartesian space at hand, which subroutine in Lapack can give the orthogonal complement of these m vectors. Orthogonal complement mean that the dot product of any vector U in the complement set and any vector v in the m-vector set at hand is zero.

I guess there are two ways to deal with this problem:

1)solve the equation Ax=0, while A is a mxn matrix whose row vectors are the m vectors at hand. But I don't know which subrout in Lapack can solve all the solutions to these underdetermined linear equations.

2)solve the equation AX=lamda*X,A is a nxn matrix whose first m rows are the m vectors the other row vectors are 0 vectors. And then find the eigenvector corresponding to the eigenvalue lamda=0. But I think this method takes a lot of time because it computes many unnecessary eigenvalues lamda/=0.

Any more efficient way? I prefer the first method!