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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 {ωi(x)} be a complete orthonormal system for the interval (a, b).
1941 R. V. Churchill Fourier Series iii. 35 The symbol {ϕr} 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).
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adj.1928
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