code: private void adjust(double[][] v, double[] vector, int corrDim) {
      double[] sum = new double[v.length];
      for(int k = 0; k < corrDim; k++) {
        plusTimesEquals(sum, v[k], transposeTimes(vector, v[k]));
      }
      v[corrDim] = normalizeEquals(minus(vector, sum));
    }
docs: Inserts the specified vector into the given orthonormal matrix
  <code>v</code> at column <code>corrDim</code>. After insertion the matrix
  <code>v</code> is orthonormalized and column <code>corrDim</code> of matrix
  <code>e_czech</code> is set to the <code>corrDim</code>-th unit vector.
  
  @param v the orthonormal matrix of the eigenvectors
  @param vector the vector to be inserted
  @param corrDim the column at which the vector should be inserted