orthonormalizev.

Brit.

/ˌɔːθə(ʊ)ˈnɔːməlʌɪz/, U.S.

/ˌɔrθoʊˈnɔrməˌlaɪz/

Forms: 1900s– orthonormalise, 1900s– orthonormalize.

Origin: Formed within English, by derivation. Etymons: orthonormal adj., -ize suffix.

Etymology: < orthonormal adj. + -ize suffix.

Mathematics.

transitive. To make (a set of vectors or functions) orthonormal by orthogonalizing them and then multiplying each by an appropriate factor.

ΘΚΠ

the world > relative properties > number > arithmetic or algebraic operations > transformation > transform [verb (transitive)] > with correspondence between quantities > in specific way

substitute1645

revert1737

transpose1810

permute1878

adjoin1888

orthogonalize1920

orthonormalize1935

perm1959

Fourier-transform1970

1935 Trans. Amer. Math. Soc. 37 309 When we orthonormalize {T^{* − 1}χ_i} we obtain {ϕ_i}.

1968 B. Kripke Introd. Anal. iii. 57 Orthonormalize the functions 1, x, x² with respect to the inner product [f, g] = ∫¹₀f(x)g(x)dx on ([0, 1]).

1993 SIAM Rev. 35 433 The process of applying T to an orthonormal basis and then orthonormalizing the result, applied repeatedly.., is called simultaneous iteration.

Derivatives

ˌorthonormaliˈzation n.

ΘΚΠ

the world > relative properties > number > mathematical number or quantity > tensor > [noun] > vector > manipulation of

orthogonalization1922

orthonormalization1942

1942 Ann. Math. 43 28 Orthonormalization of the u_{n, i} (i = 1, 2, …) will yield a sequence whose members [etc.].

1972 A. Kyrala Appl. Functions Complex Variable xiii. 318 Establish the orthonormalization relations..for the associated Legendre functions.

1990 IMA Jrnl. Numerical Anal. 10 344 In the present paper we consider the use of an orthonormalization method (ONM) for computing approximations to the mapping function f of the form [formula].

This entry has been updated (OED Third Edition, September 2004; most recently modified version published online March 2022).

单词	orthonormalize
释义	orthonormalizev. Brit. /ˌɔːθə(ʊ)ˈnɔːməlʌɪz/, U.S. /ˌɔrθoʊˈnɔrməˌlaɪz/ Forms: 1900s– orthonormalise, 1900s– orthonormalize. Origin: Formed within English, by derivation. Etymons: orthonormal adj., -ize suffix. Etymology: < orthonormal adj. + -ize suffix. Mathematics. transitive. To make (a set of vectors or functions) orthonormal by orthogonalizing them and then multiplying each by an appropriate factor. ΘΚΠ the world > relative properties > number > arithmetic or algebraic operations > transformation > transform [verb (transitive)] > with correspondence between quantities > in specific way substitute1645 revert1737 transpose1810 permute1878 adjoin1888 orthogonalize1920 orthonormalize1935 perm1959 Fourier-transform1970 1935 Trans. Amer. Math. Soc. 37 309 When we orthonormalize {T^{* − 1}χ_i} we obtain {ϕ_i}. 1968 B. Kripke Introd. Anal. iii. 57 Orthonormalize the functions 1, x, x² with respect to the inner product [f, g] = ∫¹₀f(x)g(x)dx on ([0, 1]). 1993 SIAM Rev. 35 433 The process of applying T to an orthonormal basis and then orthonormalizing the result, applied repeatedly.., is called simultaneous iteration. Derivatives ˌorthonormaliˈzation n. ΘΚΠ the world > relative properties > number > mathematical number or quantity > tensor > [noun] > vector > manipulation of orthogonalization1922 orthonormalization1942 1942 Ann. Math. 43 28 Orthonormalization of the u_{n, i} (i = 1, 2, …) will yield a sequence whose members [etc.]. 1972 A. Kyrala Appl. Functions Complex Variable xiii. 318 Establish the orthonormalization relations..for the associated Legendre functions. 1990 IMA Jrnl. Numerical Anal. 10 344 In the present paper we consider the use of an orthonormalization method (ONM) for computing approximations to the mapping function f of the form [formula]. This entry has been updated (OED Third Edition, September 2004; most recently modified version published online March 2022). < v.1935
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