We address the numerically reliable computation of generalized inverses of rational matrices in descriptor state space representation. We put a particular emphasis on two classes of inverses: the week generalized inverse and the MoorePenrose pseudoinverse. By combining the underlying computational techniques, other types of inverses of rational matrices can be computed as well. The main computa...

We prove some identities related to the reverse order law for the Moore-Penrose inverse of operators on Hilbert spaces, extending some results from (Y. Tian and S. Cheng, Linear Multilinear Algebra 52 (2004)) and (R. E. Cline, SIAM Review, Vol. 6, No. 1 (1964)) to infinite dimensional settings. 2010 Mathematics Subject Classification: 47A05, 15A09.

In this paper, we investigate properties of  with closed range satisfying the operator equations   particular, invertibility of   with where Moore-Penrose inverse of T turns out to be usual under some classes operators. We also deduce a perturbed linear operator  where  such that  has ranges and  given conditions. The relation between and null s...

In [3], Cohen, Moore and Neisendorfer analyzed the homotopy type of the mod pr Moore space P2n+1 = S2n ∪pr e2n+1 by constructing a fibration sequence Ω2S2n+1 ∂n −→ ΩFn −→ ΩP2n+1 −→ ΩS2n+1. A key result is that both ΩFn and ΩP2n+1 contain a factor which is the loop space on a one point union of Moore spaces that are at least 4n − 2 connected. Removing this factor (which can be inductively consid...

Necessary and sufficient conditions on a nearness structure are provided for which the underlying topology is developable. It is also shown that a topology is developable if and only if it admits a compatible nearness structure with a countable base. Finally it is shown that a topological space is embeddable in a complete Moore space if and only if it admits a compatible nearness structure sati...

We investigate what Ext(A, Z) can be when A is torsion-free and Hom(A, Z) = 0. We thereby give an answer to a question of Golasiński and Gonçalves which asks for the divisible Abelian groups which can be the type of a co-Moore space. 0. Introduction Marek Golasiński and Daciberg Lima Gonçalves have asked which divisible abelian groupsD can be the type of a co-Moore space [6, Problem 2.6]. In ot...

In [l] L. F. McAuley asked the following question: is it possible to partition . . . Moore's metrization theorem into three or more parts which begins with a condition for a topological space and which ends with a condition for a metrizable space, but with necessary and sufficient conditions somewhere between these extremes for semi-metric and Moore spaces? Axiom Z, stated below, is such a part...

Fluid imbalance, caused by fluid loss and changes in capillary permeability, occurs during the acute phase of burns and scalds, and the extent of the loss has been shown to depend on the body weight and surface area damaged. The blister fluid may contain protein in a concentration up to 6 g./100 ml. and sodium up to 160 mEq/l., resembling lymph and interstitial fluid in the burned patient (Cope...