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Linear mappings preserving ρ-orthogonality [PDF]
Journal of Mathematical Analysis and Applications, 2012 We define a ρ-orthogonality in a real normed space and we consider the class of linear mappings preserving this relation. We show that a linear mapping preserving ρ-orthogonality has to be a similarity, i.e., a scalar multiple of an isometry. As a result,
Paweł Wójcik
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The orthogonal flows for orthogonal iteration
Linear Algebra and its Applications, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kuo, Yueh-Cheng +2 more
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Univocal or Orthogonal Estimators of Orthogonal Factors
Psychometrika, 1963The defects of the least-squares or multiple-regression equation approach to estimating orthogonal factors are discussed and transformations of the beta weights are derived which remove these defects with minimum loss in correlations between estimators and true factor scores.
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Orthogonal sets; orthogonal contractions
Asian-European Journal of Mathematics, 2019In this paper, we are interested in obtaining fixed point theorems by keeping the orthogonal completeness of the orthogonal metric space and replacing the [Formula: see text]-contraction condition in theorems by another slightly modified conditions. The paper contains an example illustrating our results.
Eshaghi Gordji, Madjid +2 more
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Characterization of Birkhoff–James orthogonality
Journal of Mathematical Analysis and Applications, 2013 The Birkhoff-James orthogonality is a generalization of Hilbert space orthogonality to Banach spaces. We investigate this notion of orthogonality when the Banach space has more structures.
Priyanka Grover
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Orthogonal and non-orthogonal hybrids
Journal of Molecular Structure: THEOCHEM, 1988Abstract Ab initio MO wave functions for XHn molecules are analyzed in terms of the hybridization concept. It was found that for X from the first row (especially for carbon) the hybrid-AOs so obtained are close to orthogonal. If X is from the second row, different hybrids on the same atom overlap strongly and the well-known relations between degree ...
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On the Orthogonality of Classical Orthogonal Polynomials
Integral Transforms and Special Functions, 2003We consider the orthogonality of rational functions W n ( s ) as the Laplace transform images of a set of orthoexponential functions, obtained from the Jacobi polynomials, and as the Laplace transform images of the Laguerre polynomials. We prove that the orthogonality of the Jacobi and the Laguerre polynomials is induced by the orthogonality of the ...
Slobodan TriČkoviĆ, Miomir StankoviĆ
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Journal of Mathematical Physics, 1970
An essentially unique method of forming an orthonormalized set of vectors from an independent set of n vectors is presented. The resulting set is proven to maximize a certain quartic form in the original vectors.
Schweinler, H. C., Wigner, Eugene P.
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An essentially unique method of forming an orthonormalized set of vectors from an independent set of n vectors is presented. The resulting set is proven to maximize a certain quartic form in the original vectors.
Schweinler, H. C., Wigner, Eugene P.
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1966
Publisher Summary This chapter focuses on simple sets of orthogonal polynomials. These sets of polynomials arise in various ways, one of which is as the solutions of a class of differential equations. It has been shown that, under certain conditions, given any interval and a positive weight function on that interval, there exists a corresponding set ...
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Publisher Summary This chapter focuses on simple sets of orthogonal polynomials. These sets of polynomials arise in various ways, one of which is as the solutions of a class of differential equations. It has been shown that, under certain conditions, given any interval and a positive weight function on that interval, there exists a corresponding set ...
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2020 Signal Processing: Algorithms, Architectures, Arrangements, and Applications (SPA), 2020
The equation $A x=0$ tells us that x is perpendicular to every row of $A-$ and therefore to the whole row space of A. This is fundamental, but singular vectors v in the row space do more. (1) the v’s are orthogonal (2) the vectors $u=A v$ are also orthogonal (in the column space of A).
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The equation $A x=0$ tells us that x is perpendicular to every row of $A-$ and therefore to the whole row space of A. This is fundamental, but singular vectors v in the row space do more. (1) the v’s are orthogonal (2) the vectors $u=A v$ are also orthogonal (in the column space of A).
openaire +2 more sources