Spectral properties of random non-self-adjoint matrices and operators
Spectral properties of random non-self-adjoint matrices and operators
复制标题
DOI：
10.1098/rspa.2000.0662
复制
发表时间：
2000-02
期刊：
影响因子：
--
通讯作者：
E. Davies
中科院分区：
文献类型：
--
作者：
E. Davies
我描述了一些数值实验，这些实验确定了远离自伴的中型随机生成矩阵的谱不稳定性的程度。结论是，特征值很可能是本质上不可计算的类似矩阵的一个更大的大小。我还描述了一个随机家庭的有界运营商在无限维几乎所有的特征向量生成一个稠密的线性子空间，但特征值不确定的频谱。我的结果意味着非自伴安德森模型的谱在到达无限体积极限时突然改变。
I describe some numerical experiments which determine the degree of spectral instability of medium‐sized randomly generated matrices which are far from self‐adjoint. The conclusion is that the eigenvalues are likely to be intrinsically uncomputable for similar matrices of a larger size. I also describe a stochastic family of bounded operators in infinite dimensions for almost all of which the eigenvectors generate a dense linear subspace, but the eigenvalues do not determine the spectrum. My results imply that the spectrum of the non‐self‐adjoint Anderson model changes suddenly on passing to the infinite volume limit.