Let M be a compact connected special flat affine manifold without boundary equipped with a Gauduchon metric g and a covariant constant volume form. Let G be either a connected reductive complex linear algebraic group or the real locus of a split real form of a complex reductive group. We prove that a flat principal G–bundle EG over M admits a Hermitian–Einstein structure if and only if EG is po...

We consider preconditioned iterative methods applied to discretizations of the linearized Navier–Stokes equations in twoand three-dimensional bounded domains. Both unsteady and steady flows are considered. The equations are linearized by Picard iteration. We make use of the rotation form of the momentum equations, which has several advantages from the linear algebra point of view. We focus on a...

We study geometric realization questions of curvature in the affine, Riemannian, almost Hermitian, almost para Hermitian, almost hyper Hermit-ian, almost hyper para Hermitian, Hermitian, and para Hermitian settings. We also express questions in Ivanov–Petrova geometry, Osserman geometry, and curvature homogeneity in terms of geometric realizations.

This paper gives double angle theorems that bound the change in an invariant subspace of an inde nite Hermitian matrix in the graded form H = D AD subject to a perturbation H ! e H = D (A + A)D. These theorems extend recent results on a de nite Hermitian matrix in the graded form (Linear Algebra Appl., 311 (2000), 45{60) but the bounds here are more complicated in that they depend on not only r...

An m-dimensional locally conformal Khler manifold (l.c.K-manifold) is characterized as a Hermitian manifold admitting a global closed 1-form a%(called the Lee form) whose structure (F%,g%) satisfies VF -8g + 8g F + aF, where ? denotes the covariant differentiation with respect to the Hermitian metric gl, 8 -Fl a, Fl F gel and the indices 9, ,l run over the range 1,2, m. For l.c.K-manifolds, I.V...

We describe an extension to ScaLAPACK for computing with symmetric (and hermitian) matrices stored in a packed form. This is similar to the compact storage for symmetric (and hermitian) matrices available in LAPACK [2]. This enables more efficient use of memory by storing only the lower or upper triangular part of a symmetric matrix. The capabilities include Choleksy factorization (PxSPTRF) and...

We describe a new extension to ScaLAPACK [2] for computing with symmetric (Hermi-tian) matrices stored in a packed form. The new code is built upon the ScaLAPACK routines for full dense storage for a high degree of software reuse. The original ScaLAPACK stores a symmetric matrix as a full matrix but accesses only the lower or upper triangular part. The new code enables more efficient use of mem...

Classes of non-Hermitian operators that have only real eigenvalues are presented. Such operators appear in quantum mechanics and are expressed in terms of the generators of the Weyl-Heisenberg algebra. For each non-Hermitian operator A, a Hermitian involutive operator Ĵ such that A is Ĵ-Hermitian, that is, ĴA = AĴ , is found. Moreover, we construct a positive definite Hermitian Q such that A is...

By further generalizing the concept of Hermitian (or normal) and skew-Hermitian splitting for a non-Hermitian and positive-definite matrix, we introduce a new splitting, called positive-definite and skew-Hermitian (PS) splitting, and then establish a class of positivedefinite and skew-Hermitian splitting (PSS) methods similar to the Hermitian (or normal) and skew-Hermitian splitting (HSS or NSS...

We describe a new extension to ScaLAPACK [2] for computing with symmetric (Hermi-tian) matrices stored in a packed form. The new code is built upon the ScaLAPACK routines for full dense storage for a high degree of software reuse. The original ScaLAPACK stores a symmetric matrix as a full matrix but accesses only the lower or upper triangular part. The new code enables more efficient use of mem...