We consider quantum dynamical systems whose degrees of freedom are described by N × N matrices, in the planar limit N → ∞. Examples are gauge theories and the M(atrix)-theory of strings. States invariant under U(N) are 'closed strings', modelled by traces of products of matrices. We have discovered that the U(N)-invariant operators acting on both open and closed string states form a remarkable ...

The symmetry of the Hamiltonian describing the asymmetric twin model was partially studied in earlier works, and our aim here is to generalize these results for the open transfer matrix. In this spirit we first prove, that the so called boundary quantum algebra provides a symmetry for any generic – independent of the choice of model – open transfer matrix with a trivial left boundary. In additi...

Motivated by the need to formalize generation of fast running code for linear algebra applications, we show how an index-free, calculational approach to matrix algebra can be developed by regarding matrices as morphisms of a category with biproducts. This shifts the traditional view of matrices as indexed structures to a type-level perspective analogous to that of the pointfree algebra of progr...

classes of‎ ‎abaffy-broyden-spedicato (abs) methods have been introduced for‎ ‎solving linear systems of equations‎. ‎the algorithms are powerful methods for developing matrix‎ ‎factorizations and many fundamental numerical linear algebra processes‎. ‎here‎, ‎we show how to apply the abs algorithms to devise algorithms to compute the wz and zw‎ ‎factorizations of a nonsingular matrix as well as...

classes of‎ ‎abaffy-broyden-spedicato (abs) methods have been introduced for‎ ‎solving linear systems of equations‎. ‎the algorithms are powerful methods for developing matrix‎ ‎factorizations and many fundamental numerical linear algebra processes‎. ‎here‎, ‎we show how to apply the abs algorithms to devise algorithms to compute the wz and zw‎ ‎factorizations of a nonsingular matrix as well as...

We examine the picture of emergent gravity arising from a mass deformed matrix model. Due to the mass deformation, a vacuum geometry turns out to be a constant curvature spacetime such as d-dimensional sphere and (anti-)de Sitter spaces. We show that the mass deformed matrix model giving rise to the constant curvature spacetime can be derived from the d-dimensional Snyder algebra. The emergent ...

GPUs are dedicated processors used for complex calculations and simulations and they can be effectively used for tropical algebra computations. Tropical algebra is based on max-plus algebra and minplus algebra. In this paper we proposed and designed a library based on Tropical Algebra which is used to provide standard vector and matrix operations namely Basic Tropical Algebra Subroutines (BTAS)...

Advanced algebra is a required course of undergraduate mathematics, which plays fundamental role in completing the study other professional courses for students. Matrix theory an important branch it not only basic subject, but also themost practical value. Widely used mathematical theory, matrix concept major algebra, Positive definite kind matrix, occupies position higher its has rich content,...

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We extend the correspondence between double Lie algebras and skew-symmetric Rota-Baxter operators of weight 0 on matrix algebra for infinite-dimensional case. give first example a simple algebra.