We establish the orthogonality of the range and the kernel of a normal derivation with respect to the unitarily invariant norms associated with norm ideals of operators. Related orthogonality results for certain nonnormal derivations are also given.

Abs t rac t -P roper t i e s of nonlinear multiobjective problems implied by the Karush-Kuhn-Tucker necessary conditions are investigated. It is shown that trajectories of Lagrange multipliers corresponding to the components of the vector cost function are orthogonal to the corresponding trajectories of vector deviations in the balance space (to the balance set for Pareto solutions). ~) 2003 El...

In updating algorthms where orthogonal transformations are accumulated , it is important to preserve the orthogonality of the product in the presence of rounding error. Moonen, Van Dooren, and Vandewalle have pointed out that simply normalizing the columns of the product tends to preserve orthogonality | though not, as DeGroat points out, to working precision. In this note we give an analysis o...

We examined the kinetics of the catalytic activities of aspartate aminotransferase (AST, EC 2.6.1.1) isoenzymes in serum of 28 patients with myocardial infarction who were to receive either intracoronary urokinase--reperfusion angiographically proved--or conventional therapy (control group). Cytosolic (soluble) AST (s-AST) activity in serum increased rapidly immediately after recanalization, re...

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Let A and B be rectangular matrices. Then A is orthogonal to B if II A + f-LB II ?: II A II for every scalar f-L. Some approximation theory and convexity results on matrices are used to study orthogonality of matrices and answer an open problem of Bhatia and Semrl. © 2002 Elsevier Science Inc. All rights reserved.