A modified Gauss's algorithm for solving a system of linear equations in an integral ring is proposed, as well as an appropriate algorithm for calculating the elements of the adjoint matrix.

We solve the non-local eigenvalue problem that arose from consideration of the adjoint sector of the c = 1 matrix model in [1]. We obtain the exact wavefunction and a scattering phase that matches the string theory calculation.

We study the decay of eigenfunctions of the non self-adjoint matrix operator H = ( −∆+μ+U W −W ∆−μ−U ) , for μ > 0, corresponding to eigenvalues in the strip −μ < ReE < μ.

We utilize group-theoretical methods to develop a matrix representation of differential operators that act on tensors of any rank. In particular, we concentrate on the matrix formulation of the curl operator. A self-adjoint matrix of the curl operator is constructed and its action is extended to a complex plane. This scheme allows us to obtain properties, similar to those of the traditional cur...

In this paper we derive canonical forms under structure preserving equivalence transformations for matrices and matrix pencils that have a multiple structure, which is either an H-selfadjoint or H-skew-adjoint structure, where the matrix H is a complex nonsingular Hermitian or skew-Hermitian matrix. Matrices and pencils of such multiple structures arise for example in quantum chemistry in Hartr...

We develop the basic theory of matrix-valued Weyl–Titchmarsh M-functions and the associated Green’s matrices for whole-line and half-line self-adjoint Hamiltonian finite difference systems with separated boundary conditions.

We prove a full large deviations principle in the scale N for the empirical measure of the eigenvalues of an N N non self adjoint matrix composed of i i d zero mean random variables with variance N The good rate function which governs this rate func tion possesses as unique minimizer the circular law providing an alter native proof of convergence to the latter The techniques are related to rece...

Throughout this paper, G denotes a simple and simply connected algebraic group over C of rank r and H is a Cartan subgroup, with Lie algebras g = LieG and h = LieH. Let R be the root system of the pair (G,H), W the Weyl group, and Λ ⊆ h the coroot lattice. Fix once and for all a positive Weyl chamber, i.e. a set of simple roots ∆. The geometric invariant theory quotient of g by the adjoint acti...

‎This paper considers a non-local initial-boundary value problem containing a first order partial differential equation with variable coefficients‎. ‎At first‎, ‎the non-self-adjoint spectral problem is derived‎. ‎Then its adjoint problem is calculated‎. ‎After that‎, ‎for the adjoint problem the associated eigenvalues and the subsequent eigenfunctions are determined‎. ‎Finally the convergence ...