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Jacobis method is a well-known algorithm in linear algebra to diagonalize symmetric matrices by successive elementary rotations. We report about the generalization of these elementary rotations towards canonical transformations acting in Hamiltonian phase spaces. This generalization allows to use Jacobis method in order to compute eigenvalues and eigenvectors of Hamiltonian (and skew-Hamiltonian) matrices with either purely real or purely imaginary eigenvalues by successive elementary symplectic decoupling-transformations.
For a two-parameter family of Jacobi matrices exhibiting first-order spectral phase transitions, we prove discreteness of the spectrum in the positive real axis when the parameters are in one of the transition boundaries. To this end we develop a met
Using properties of skew-Hamiltonian matrices and classic connectedness results, we prove that the moduli space $M_{ort}^0(r,n)$ of stable rank $r$ orthogonal vector bundles on $mathbb{P}^2$, with Chern classes $(c_1,c_2)=(0,n)$, and trivial splittin
By using the quasi-determinant the construction of Gelfand et al. leads to the inverse of a matrix with noncommuting entries. In this work we offer a new method that is more suitable for physical purposes and motivated by deformation quantization, wh
We are interested in the phenomenon of the essential spectrum instability for a class of unbounded (block) Jacobi matrices. We give a series of sufficient conditions for the matrices from certain classes to have a discrete spectrum on a half-axis of
We propose two ways for determining the Greens matrix for problems admitting Hamiltonians that have infinite symmetric tridiagonal (i.e. Jacobi) matrix form on some basis representation. In addition to the recurrence relation comming from the Jacobi-