求解特征值对应的特征向量

求助，请大佬指导！
pcl中有计算特征值对应的特征向量的方法，如下：

template <typename Matrix, typename Vector> inline void
pcl::computeCorrespondingEigenVector (const Matrix& mat, const typename Matrix::Scalar& eigenvalue, Vector& eigenvector)
{
  typedef typename Matrix::Scalar Scalar;
  // Scale the matrix so its entries are in [-1,1].  The scaling is applied
  // only when at least one matrix entry has magnitude larger than 1.

  Scalar scale = mat.cwiseAbs ().maxCoeff ();
  if (scale <= std::numeric_limits < Scalar > ::min ())
    scale = Scalar (1.0);

  Matrix scaledMat = mat / scale;

  scaledMat.diagonal ().array () -= eigenvalue / scale;

  Vector vec1 = scaledMat.row (0).cross (scaledMat.row (1));
  Vector vec2 = scaledMat.row (0).cross (scaledMat.row (2));
  Vector vec3 = scaledMat.row (1).cross (scaledMat.row (2));

  Scalar len1 = vec1.squaredNorm ();
  Scalar len2 = vec2.squaredNorm ();
  Scalar len3 = vec3.squaredNorm ();

  if (len1 >= len2 && len1 >= len3)
    eigenvector = vec1 / std::sqrt (len1);
  else if (len2 >= len1 && len2 >= len3)
    eigenvector = vec2 / std::sqrt (len2);
  else
    eigenvector = vec3 / std::sqrt (len3);
}

先计算A-aE，a为对应的特征值
然后计算0行与1行的叉乘，0和2的叉乘，1和2的叉乘
并且取这三者二范数最大的向量作为特征向量，并且进行单位化。

这里不清楚为什么要取最大值最为特征向量，有明白的请在评论区指出，谢谢！