orthonormaladj.

Brit.

/ˌɔːθə(ʊ)ˈnɔːml/, U.S.

/ˌɔrθoʊˈnɔrm(ə)l/

Origin: Formed within English, by compounding. Etymons: orthogonal adj., normal adj.

Etymology: < ortho- (in orthogonal adj.) + normal adj.

Mathematics.

Of a set, esp. a basis for a vector space: such that any two elements are orthogonal and that the inner product of any element with itself is unity.

ΘΚΠ

the world > relative properties > number > mathematical number or quantity > numerical arrangement > [adjective] > of sets

tantipartite1858

connected1893

measurable1901

ordered1901

well-ordered1901

null1903

empty1905

closed1909

orthonormal1928

matroid1935

recursively enumerable1936

simple1936

disjoint1937

partially ordered1941

1928 Proc. National Acad. Sci. U.S.A. 14 911 Let {ω_i(x)} be a complete orthonormal system for the interval (a, b).

1941 R. V. Churchill Fourier Series iii. 35 The symbol {ϕ_r} will be used to denote an orthonormal set whose vectors are ϕ₁, ϕ₂, and ϕ₃. The simplest example of such a set is that consisting of the unit vectors along the three coordinate axes.

1965 E. M. Patterson & D. E. Rutherford Elem. Abstr. Algebra v. 173 It is frequently desirable to choose an orthonormal basis: that is, a basis of which each vector is of unit length..and such that any two basic vectors are orthogonal.

1972 M. Kline Math. Thought xlv. 1063 The eigenfunctions associated with the separate eigenvalues can be chosen to be an orthonormal (orthogonal and normalized) set.

2001 F. A. Morrison Understanding Rheol. ii. 22 Vector multiplication is..much easier to carry out when the vectors are written with respect to orthonormal coordinate systems.

Derivatives

orthonorˈmality n. the property of being orthonormal.

ΘΚΠ

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

orthonormality1935

1935 Amer. Jrnl. Math. 57 869 We..impose on them the conditions of M-orthonormality.

1959 G. Troup Masers ii. 16 This orthonormality is an expression of the independence of the stationary states.

1997 RAND Jrnl. Econ. 28 s152 One statistical way to resolve this lack of identification of price and characteristics parameters is to impose mutual orthonormality on the characteristics vectors (mutual orthogonality and restriction to unit length).

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

单词	orthonormal
释义	orthonormaladj. Brit. /ˌɔːθə(ʊ)ˈnɔːml/, U.S. /ˌɔrθoʊˈnɔrm(ə)l/ Origin: Formed within English, by compounding. Etymons: orthogonal adj., normal adj. Etymology: < ortho- (in orthogonal adj.) + normal adj. Mathematics. Of a set, esp. a basis for a vector space: such that any two elements are orthogonal and that the inner product of any element with itself is unity. ΘΚΠ the world > relative properties > number > mathematical number or quantity > numerical arrangement > [adjective] > of sets tantipartite1858 connected1893 measurable1901 ordered1901 well-ordered1901 null1903 empty1905 closed1909 orthonormal1928 matroid1935 recursively enumerable1936 simple1936 disjoint1937 partially ordered1941 1928 Proc. National Acad. Sci. U.S.A. 14 911 Let {ω_i(x)} be a complete orthonormal system for the interval (a, b). 1941 R. V. Churchill Fourier Series iii. 35 The symbol {ϕ_r} will be used to denote an orthonormal set whose vectors are ϕ₁, ϕ₂, and ϕ₃. The simplest example of such a set is that consisting of the unit vectors along the three coordinate axes. 1965 E. M. Patterson & D. E. Rutherford Elem. Abstr. Algebra v. 173 It is frequently desirable to choose an orthonormal basis: that is, a basis of which each vector is of unit length..and such that any two basic vectors are orthogonal. 1972 M. Kline Math. Thought xlv. 1063 The eigenfunctions associated with the separate eigenvalues can be chosen to be an orthonormal (orthogonal and normalized) set. 2001 F. A. Morrison Understanding Rheol. ii. 22 Vector multiplication is..much easier to carry out when the vectors are written with respect to orthonormal coordinate systems. Derivatives orthonorˈmality n. the property of being orthonormal. ΘΚΠ the world > relative properties > number > mathematical number or quantity > tensor > [noun] > vector > property of orthonormality1935 1935 Amer. Jrnl. Math. 57 869 We..impose on them the conditions of M-orthonormality. 1959 G. Troup Masers ii. 16 This orthonormality is an expression of the independence of the stationary states. 1997 RAND Jrnl. Econ. 28 s152 One statistical way to resolve this lack of identification of price and characteristics parameters is to impose mutual orthonormality on the characteristics vectors (mutual orthogonality and restriction to unit length). This entry has been updated (OED Third Edition, September 2004; most recently modified version published online March 2022). < adj.1928
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