Eigenvalues of non‐Hermitian matrices: A dynamical and an iterative approach—Application to a truncated Swanson model

@article{Bagarello2020EigenvaluesON,
  title={Eigenvalues of non‐Hermitian matrices: A dynamical and an iterative approach—Application to a truncated Swanson model},
  author={Fabio Bagarello and Francesco Gargano},
  journal={Mathematical Methods in the Applied Sciences},
  year={2020},
  volume={43},
  pages={5758 - 5775}
}
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 dynamical approach, based on a pair of ordinary differential equations defined in terms of the matrix A and of its adjoint A† . Then, we consider an extension of the so‐called… 
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References

SHOWING 1-10 OF 31 REFERENCES
Eigenvalue computation in the 20th century
PT Symmetry
A REMARK ON WANG’S FRACTAL VARIATIONAL PRINCIPLE
Wang et al. established successfully a variational principle in a fractal space by the semi-inverse method. This paper argues that in the fractal space, time should be also considered as a fractal,...
A dichotomy result about Hessenberg matrices associated with measures in the unit circle
We characterize Hessenberg matrices D associated with measures in the unit circle ν, which are matrix representations of compact and actually Hilbert Schmidt perturbations of the forward shift
A VARIATIONAL FORMULATION FOR ANISOTROPIC WAVE TRAVELING IN A POROUS MEDIUM
An anisotropic wave in a porous medium is a hot topic in the coastal protection. A fractal derivative model is established, and a variational principle is established for the anisotropic wave
Quantum Mechanics
An introduction to frames and Riesz bases
Frames in Finite-dimensional Inner Product Spaces.- Infinite-dimensional Vector Spaces and Sequences.- Bases.- Bases and their Limitations.- Frames in Hilbert Spaces.- Tight Frames and Dual Frame
Methods of Modern Mathematical Physics. I: Functional Analysis
Small eigenvalues of large Hermitian moment matrices
...
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