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 ...
这个原本non-Hermitian的matrix就看起来像Hermitian Matrix一样了。另外，如果我们可以找到一个新的positive...
通过\Theta，我们可以定义如下一个新的metric：那么，在这个新的metric下，这个原本non-Hermitian的matrix...
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 response provides high sensitivity to small perturbations and...
However, in most of the prospective applications that we have in mind we work with a finite-dimensional matrix form of the so-called "Hermitian" operator, in which case there is no longer any need for such mathematical precision. Marginally, let us note here that, even in the infinite- ...
Then, we perform a direct diagonalization of finite hyperbolic clusters with different mass terms, and numerical results are presented in Fig.2a(m = 0.7,a = 0.2) and Fig.2b(m = 0.7,a = 3.2) with blue circles. For comparation, we also explore hyperbolic band theory with...
It is well known that the entries of the inverse of a Hermitian positive definite, banded matrix exhibit a decay away from the main diagonal if the condition number of the matrix is not too large compared to the matrix size. There is a rich literature on bounds which predict and explain ...
The idea of these two algorithms is based on the so-called Jacobi algorithm for solving the eigenvalues problem of Hermitian matrix. The algorithms are then called ‘general Jabobi-like diagonalization’ algorithms (GERALD). They are based on the search of two complex parameters by the ...
hermitian, the diagonalization requires a large amount of CPU-time.A version of the de,ated Arnoldi algorithm has been applied to quantum spin chains for the ,rst time here. The Arnoldi algorithm that reduces to the Lanczos algorithm in the case of hermitian matrices was already used for the...
(2 + 1) yields a different flag manifold RP2and is relevant for the Floquet Euler phase14. Other tantalizing extensions include the 3D nodal-line metals8characterized by non-Abelian frame charges and non-Hermitian phases with non-Abelian band braidings51,52,53by relaxing the PT symmetry ...