Definition of orthonormal in English:

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orthonormal

Pronunciation: /ˌôrTHōˈnôrməl/

adjective

Mathematics
Both orthogonal and normalized.
Example sentences
  • He also expanded functions related to the integral of the kernel function as an infinite series in a set of orthonormal eigenfunctions.
  • He also studied orthonormal series and topology.
  • Fig.4 A shows the four orthonormal basis spectra with highest singular values (U spectra, see Material and Methods).

Derivatives

orthonormality

Pronunciation: /-nôrˈmalitē/
noun
Example sentences
  • The orthonormality condition ensures that minimization along any given direction vector does not jeopardize the minimization along another direction vector within this set.
  • The modes are defined by weighting patterns together with some appropriate restrictions (orthonormality) as shown in the following.
  • On the other hand, repeated computing of scalar products in (3) and (5) help to check orthonormality at every stage.

orthonormalization

Pronunciation: /-ˌnôrməliˈzāSHən/
noun
Example sentences
  • In this paper he gave what is now called the Gram Schmidt orthonormalisation process for constructing an orthonormal set of functions from a linearly independent set.
  • The set { 1,…, k } can be transformed into a mutually orthonormal set of vectors given by { 1,…,’ k } using the Gram-Schmidt orthonormalization procedure.
  • n the present study, a numeric orthonormalisation method for calculating this and similar problems is tested in order to resolve the stiffness.

For editors and proofreaders

Syllabification: or·tho·nor·mal

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