论文标题
非铁矩阵的特征值：一种动力学和迭代方法。应用于截短的斯旺森型号
Eigenvalues of non-hermitian matrices: a dynamical and an iterative approach. Application to a truncated Swanson model
论文作者
论文摘要
我们提出了两种不同的策略，以查找给定（不一定是Hermitian）矩阵$ a $的特征值和特征向量。我们的方法也适用于复杂的特征值，使得对物理应用的应用有趣，尤其是伪造量子力学。我们首先考虑一种{\ em dynalical}方法，基于根据矩阵$ a $及其伴随$ a^\匕首$定义的一对普通微分方程。然后，我们考虑了所谓的功率方法的扩展，为此，我们证明了$ a \ neq a^\匕首$的固定点定理，可用于确定$ a $ a $ a $ a $ a $ a $ a^\ dagger $的特征值。这两种策略应用于一些明确的问题。特别是，我们计算由最近提出的量子机械系统（{\ em em thuncated swanson型号}产生的基质的特征值和特征向量，并检查了Hessenberg矩阵的一些渐近特征。
We propose two different strategies to find eigenvalues and eigenvectors of a given, not necessarily Hermitian, matrix $A$. Our methods apply also to the case of complex eigenvalues, making the strategies interesting for applications to physics, and to pseudo-hermitian quantum mechanics in particular. We first consider a {\em dynamical} approach, based on a pair of ordinary differential equations defined in terms of the matrix $A$ and of its adjoint $A^\dagger$. Then we consider an extension of the so-called power method, for which we prove a fixed point theorem for $A\neq A^\dagger$ useful in the determination of the eigenvalues of $A$ and $A^\dagger$. The two strategies are applied to some explicit problems. In particular, we compute the eigenvalues and the eigenvectors of the matrix arising from a recently proposed quantum mechanical system, the {\em truncated Swanson model}, and we check some asymptotic features of the Hessenberg matrix.
