We introduce and develop a theory of orthogonality with respect to Sobolev inner products on the real line for sequences functions tridiagonal, skew-Hermitian differentiation matrix. While such L2 -orthogonal systems is well established, requires new concepts their analysis. characterize completely as appropriately weighted Fourier transforms orthogonal polynomials present number illustrative e...

We find geometric conditions on a four-dimensional Hermitian manifold endowed with metric connection totally skew-symmetric torsion under which the complex structure is harmonic map from into its twistor space considered natural family of Riemannian metrics defined by means and given base manifold.

Let H be the real quaternion algebra and Hm×n denote set of all m×n matrices over H. For A?Hm×n, we by A? n×m matrix obtained applying ? entrywise to transposed AT, where is a non-standard involution A?Hn×n said ?-skew-Hermicity if A=?A?. In this paper, provide some necessary sufficient conditions for existence ?-skew-Hermitian solution system equations with four unknowns AiXi(Ai)?+BiXi+1(Bi)?=...

The sensitivity of a multiple eigenvalue of a matrix under perturbations can be measured by its Hölder condition number. Various extensions of this concept are considered. A meaningful notion of structured Hölder condition numbers is introduced and it is shown that many existing results on structured condition numbers for simple eigenvalues carry over to multiple eigenvalues. The structures inv...