-Invariant tensors and graphs
We describe a correspondence between -invariant tensors and graphs. We then show how this correspondence accommodates various types of symmetries and orientations.
Gap universality of generalized Wigner and -ensembles
We consider generalized Wigner ensembles and general -ensembles with analytic potentials for any . The recent universality results in particular assert that the local averages of consecutive eigenvalue gaps in the bulk of the spectrum are universal in the sense that they coincide with those of the corresponding Gaussian -ensembles. In this article, we show that local averaging is not necessary for this result, i.e. we prove that the single gap distributions in the bulk are universal. In fact,...
Gauss sums and the matrix equation over fields of characteristic two
Gauss sums and the number of solutions to the matrix equation over
Gaussian fluctuations in complex sample covariance matrices.
Gaussian fluctuations of eigenvalues in the GUE
Gcd-closed sets and determinants of matrices associated with arithmetical functions
Gegenbauer matrix polynomials and second order matrix differential equations.
Gegenbauer polynomials and semiseparable matrices.
General construction of Banach-Grassmann algebras
We show that a free graded commutative Banach algebra over a (purely odd) Banach space is a Banach-Grassmann algebra in the sense of Jadczyk and Pilch if and only if is infinite-dimensional. Thus, a large amount of new examples of separable Banach-Grassmann algebras arise in addition to the only one example previously known due to A. Rogers.
General preservers of quasi-commutativity on Hermitian matrices.
General theory of Lie derivatives for Lorentz tensors
We show how the ad hoc prescriptions appearing in 2001 for the Lie derivative of Lorentz tensors are a direct consequence of the Kosmann lift defined earlier, in a much more general setting encompassing older results of Y. Kosmann about Lie derivatives of spinors.
Generalización de los teoremas de alternativa de sistemas de inecuaciones lineales.
Generalization of Scott's permanent identity.
Generalization of the Bauer-Fike Theorem.
Generalizations of Milne’s -Chu-Vandermonde summation
We derive two identities for multiple basic hyper-geometric series associated with the unitary group. In order to get the two identities, we first present two known -exponential operator identities which were established in our earlier paper. From the two identities and combining them with the two -Chu-Vandermonde summations established by Milne, we arrive at our...
Generalizations of Nekrasov matrices and applications
In this paper we present a nonsingularity result which is a generalization of Nekrasov property by using two different permutations of the index set. The main motivation comes from the following observation: matrices that are Nekrasov matrices up to the same permutations of rows and columns, are nonsingular. But, testing all the permutations of the index set for the given matrix is too expensive. So, in some cases, our new nonsingularity criterion allows us to use the results already calculated...
Generalized approximation numbers
Generalized Bezoutian for a periodic collection of rational matrices
Generalized Catalan numbers, Hankel transforms and Somos-4 sequences.