Abstract: It is given that a simplistic proof for the solvability of Total Least Squares problem, extending this idea for General Total Least Squares problem, establishes a sufficient and necessary condition for solvability, proves the uniqueness of the amendment matrix and gives it's expression.

Key words: general total least squares problem, SVD decomposition, singular values, singular vectors

摘要： 给出了完全最小二乘问题可解性的一个简洁证明，并将这一证明思想推广到广义完全最小二乘问题上，建立了它的可解性理论，内容包括广义完全最小二乘问题可解的充分必要条件和校正矩阵的唯一性及其表达式。

关键词: 广义完全最小二乘问题, 奇异值分解, 奇异值, 奇异向量