我就单纯把我知道的关于non-Hermitian matrix的计算写下来,希望能起到抛砖引玉的效果了。 首先,一个non-Hermitian的Hamiltonian的eigenvalue spectrum不一定是real的,甚至是incomplete的。这种情况的计算我不懂,希望有人能指点一下。 但是non-Hermitian Hamiltonian有一些特殊的情况下会有real spectrum,这种Hamiltonian被...
Non-Hermitian matrixLeast-squaresCanonical polyadic decompositionJoint blind source separationA non-orthogonal approximate joint diagonalization (AJD) algorithm of a set of non-Hermitian matrices is presented. Specifically, the proposed algorithm aims to find two distinct general (not necessarily orthogonal ...
The primary challenge is that the eigenvectors of a non-Hermitian matrix can be non-unitary, leading to instances where the use of unitary gate-based quantum methods fails to identify the eigenvector matrix required for matrix diagonalization. Further, power system small signal analysis requires ...
We establish a general relation between the diagonal correlator of eigenvectors and the spectral Green's function for non-hermitian random-matrix models in the large-N limit. We apply this result to a number of non-hermitian random-matrix models and show that the outcome is in good agreement ...
point附近，没法对角化只能求jordan 标准型 数值上，用matlab里vpa包手动提高数值精度就行了。
摘要: Let W(T) and r(T) denote the numerical range and numerical radius of an n x n complex matrix T. Let H 关键词: definite Hermitian pair nondiagonalizable numerical range numerical radius Crawford number DOI: 10.1137/040616346 被引量: 4 ...
Exceptional point degeneracies (EPDs) in the resonant spectrum of non-Hermitian systems have been recently employed for sensing due to the sublinear response of the resonance splitting when a perturbant interacts with the sensor. The sublinear
This algorithm successively finds the optimal Givens and hyperbolic rotation matrices that constitute the elementary rotation matrix in each iteration in an alternating manner. It does not require the target matrices to be Hermitian, and thus could be well adapted to BSS problems that involve fourth-...
Normal-ordering for Hubbard models can introduce small deviations from Hermitian matrices. Why? (Fixed!) For non-interacting systems, compute LIOMs with ED as a comparison/test? Add creation/annihilation operators (factor of N cheaper than number operators to compute). Add long-range couplings fro...
2. Arnoldi method and function approximation for a non-Hermitian matrix A numerical implementation of the sign function using the spectral definition (1.4) is only possible for small matrices, as a full diagonalization becomes too expensive as the matrix grows. Alternatively, matrix-based ...