orthogonalizationn.
/ɔːˌθɒɡənl̩ʌɪˈzeɪʃn/, U.S. /ɔrˌθɑɡənəˌlaɪˈzeɪʃ(ə)n/, /ɔrˌθɑɡənələˈzeɪʃ(ə)n/ The process of orthogonalizing something; (Mathematics) the procedure of constructing an orthogonal set of functions or vectors from ones that are linearly independent but not orthogonal.
ΘΚΠ
the world > relative properties > number > mathematical number or quantity > tensor > [noun] > vector > manipulation of
orthogonalization1922
orthonormalization1942
1922 Proc. London Math. Soc. 21 97 We have now only to derive from {χn(t)} a new set {ψn(t)} by the ‘orthogonalisation method’ of Mr. E. Schmidt to get a complete, orthogonal, and normalised set possessing the property (3).
1966 G. Arfken Math. Methods for Physicists ix. 342 Consider two (nonparallel) vectors A and B in the xy-plane. We may normalize A to unit magnitude and then form B′ = aA + B so that B′ is perpendicular to A. By normalizing B′ we have completed the Schmidt orthogonalization for two vectors.
1987 R. Livi et al. in G. Busiello et al. Internat. Meeting Adv. on Phase Transitions 519 A Gram–Schmidt orthogonalization procedure is applied at fixed time intervals.
1998 P. McLeod et al. Introd. Connectionist Modelling Cognitive Processes vi. 134 By allocating separate output units to somewhat related input patterns, a competitive network can produce a set of outputs which are less correlated than the inputs—orthogonalisation.
This entry has been updated (OED Third Edition, September 2004; most recently modified version published online March 2022).
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n.1922