Studies on matrix diagonalization by solving nonlinear systems

矩阵对角化，如特征值分解、奇异值分解等，是线性代数中的基本问题，也是应用于各个领域的重要工具。在本研究中，我们提出了一种新的方法，称为超平面约束方法。该方法通过用牛顿法求解约束在超平面上的非线性系统，得到矩阵对角化。通过选择合适的超平面法向量，避免了牛顿法选择初始向量的问题。

The matrix diagonalizations, for example eigenvalue decomposition, singular value decomposition, are basic topics in linear algebra, and they also important tools in various fields. In this research, we developed new method, which is called the hyperplane-constrained method. This method can obtain matrix diagonalization by solving the nonlinear systems, which are constrained on hyperplanes, by the Newton method. The problems on selecting initial vectors of the Newton method is avoided by suitable selecting the normal vectors of the hyperplanes.