We generalize the array orthogonality property for perfect autocorrelation sequences to n-dimensional arrays. The generalized array orthogonality property is used to derive a number of ndimensional perfect array constructions.

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...

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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.

The class of shape equivalences for a pair (C,K) of categories is the orthogonal of K, that is Σ = K. Then Σ is internally saturated (Σ = Σ). On the other hand, every internally saturated class of morphisms Σ ⊂ Mor(C), is the class of shape equivalences for some pair (C,K). Moreover, every class of shape equivalences Σ enjoys a calculus of left fractions and such a fact allows one to use techni...

Adámek and Sousa recently solved the problem of characterizing the subcategories K of a locally λ-presentable category C which are λ-orthogonal in C, using their concept of Kλ-pure morphism. We strenghten the latter definition, in order to obtain a characterization of the classes defined by orthogonality with respect to λ-presentable morphisms (where f :A B is called λ-presentable if it is a λ-...