Full rank factorization and the Flanders theorem.
Further determinant identities related to classical root systems
By introducing polynomials in matrix entries, six determinants are evaluated which may be considered extensions of Vandermonde-like determinants related to the classical root systems.
Further results on the Craig-Sakamoto equation.
Further results on the reverse order law for -inverse and -inverse of a matrix product.
Fuzzy transforms in image compression and fusion
An overview of direct and inverse fuzzy transforms of three types is given and applications to data processing are considered. The construction and some important properties of fuzzy transforms are presented on the theoretical level. Three applications of -transform to data processing have been chosen: compressional and reconstruction of data, removing noise and data fusion. All of them successively exploit the filtering property of the inverse fuzzy transform.
-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.