Definition & Betydelse | Engelska ordet ORTHOGONALITY

Definition av ORTHOGONALITY

1. (matematik) ortogonalitet

Exempel på hur man kan använda ORTHOGONALITY i en mening

• Inner products allow formal definitions of intuitive geometric notions, such as lengths, angles, and orthogonality (zero inner product) of vectors.
• Closely related and important geometrical concepts are perpendicular lines, meaning lines that form right angles at their point of intersection, and orthogonality, which is the property of forming right angles, usually applied to vectors.
• Finally, by defining them via orthogonality with respect to the most obvious weight function on a finite interval, it sets up the Legendre polynomials as one of the three classical orthogonal polynomial systems.
• Alternatively, when the inner product of the function being approximated cannot be evaluated, the discrete orthogonality condition gives an often useful result for approximate coefficients:.
• Other uses of normalizing constants include making the value of a Legendre polynomial at 1 and in the orthogonality of orthonormal functions.
• This concept of orthogonality in combinatorics is strongly related to the concept of blocking in statistics, which ensures that independent variables are truly independent with no hidden confounding correlations.
• The lemma is named after Issai Schur who used it to prove the Schur orthogonality relations and develop the basics of the representation theory of finite groups.
• Under the Petersson metric it is shown that we can define the orthogonality on the space of modular forms as the space of cusp forms and its orthogonal space and they have finite dimensions.
• In geometry, the relation of hyperbolic orthogonality between two lines separated by the asymptotes of a hyperbola is a concept used in special relativity to define simultaneous events.
• In appending a time dimension to three-dimensional space, he specified an alternative perpendicularity, hyperbolic orthogonality.
• Despite differences in their approaches, these derivations share a common topic—proving the orthogonality of the residuals and conjugacy of the search directions.
• Steger and Sorenson (1980) proposed a volume orthogonality method that uses Hyperbolic PDEs for mesh generation.
• Book XI develops notions of orthogonality and parallelism of lines and planes, and defines solids including parallelpipeds, pyramids, prisms, spheres, octahedra, icosahedra and dodecahedra.
• In Minkowski's view, the naïve notion of velocity is replaced with rapidity, and the ordinary sense of simultaneity becomes dependent on hyperbolic orthogonality of spatial directions to the worldline associated to the rapidity.
• The resulting similarity ranges from -1 meaning exactly opposite, to 1 meaning exactly the same, with 0 indicating orthogonality or decorrelation, while in-between values indicate intermediate similarity or dissimilarity.
• Notions from Shelah's classification program, such as regular types, forking, and orthogonality, allowed these ideas to be carried to greater generality, especially in superstable theories.
• These projections are bounded, self-adjoint, idempotent operators that satisfy the orthogonality condition.
• As perpendicularity is the relation of conjugate diameters of a circle, so hyperbolic orthogonality is the relation of conjugate diameters of rectangular hyperbolas.
• Note that two submanifolds of codimension 1 are orthogonal if their normal vectors are orthogonal and in a nondefinite metric orthogonality does not imply transversality.
• This identity no longer holds in general Banach spaces, however one can introduce a notion of orthogonality probabilistically with the help of Rademacher random variables, for this reason one also speaks of Rademacher type and Rademacher cotype.

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