several representations of the generalized drazin inverse of an anti-triangular block matrix in banach algebra are given in terms of the generalized banachiewicz--schur form.

Using the generalized Hamiltonian method of Batalin, Fradkin and Vilkovsky we develop the BRST formalism for the bosonic string on AdS5×S formulated as principal chiral model. Then we show that the monodromy matrix and non-local charges are BRST invariant.

The theory of Bogoliubov is generalized for the case of a weakly-interacting Bose-gas in harmonic trap. A set of nonlinear matrix equations is obtained to make the diagonalization of Hamiltonian possible. Its perturbative solution is used for the calculation of the energy and the condensate fraction of the model system to show the applicability of the method.

In this paper, an iterative method is proposed for solving the matrix inverse problem AX = B for Hermitian-generalized Hamiltonian matrices with a submatrix constraint. By this iterative method, for any initial matrix A0, a solution A ∗ can be obtained in finite iteration steps in the absence of roundoff errors, and the solution with least norm can be obtained by choosing a special kind of init...

Generalized matrix functions (GMFs) extend the concept of a matrix function to rectangular matrices via the singular value decomposition. Several applications involving directed graphs, Hamiltonian dynamical systems, and optimization problems with low-rank constraints require the action of a GMF of a large, sparse matrix on a vector. We present a new method for applying GMFs to vectors based on...

the rank-k numerical range has a close connection to the construction of quantum error correction code for a noisy quantum channel. for noisy quantum channel, a quantum error correcting code of dimension k exists if and only if the associated joint rank-k numerical range is non-empty. in this paper the notion of joint rank-k numerical range is generalized and some statements of [2011, generaliz...

This paper introduces generalized canonical transformations for generalized Hamiltonian systems which convert a generalized Hamiltonian system into another one, and preserve the generalized Hamiltonian structure of the original. As in classical mechanics it is expected that canonical transformations will provide new insights and fundamental tools for both analysis and synthesis of those systems...

The two-sided Rayleigh quotient iteration proposed by Ostrowski computes a pair of corresponding left-right eigenvectors of a matrix C. We propose a Grassmannian version of this iteration, i.e., its iterates are pairs of p-dimensional subspaces instead of one-dimensional subspaces in the classical case. The new iteration generically converges locally cubically to the pairs of left-right p-dimen...

The construction of a family of real Hamiltonian forms (RHF) for the special class of affine 1+ 1-dimensional Toda field theories (ATFT) is reported. Thus the method, proposed in [1] for systems with finite number of degrees of freedom is generalized to infinitedimensional Hamiltonian systems. The construction method is illustrated on the explicit nontrivial example of RHF of ATFT related to th...