| 单词 |
orthogonalization |
| 释义 |
orˌthogonaliˈzation Math.
[f. as prec. + -ization.]
The procedure of constructing an orthogonal set of functions or vectors from ones that are linearly independent but not orthogonal.
1922Proc. London Math. Soc. XXI. 97 We have now only to derive from {ob}χn(t){cb} a new set {ob}ψn(t){cb} by the ‘orthogonalisation method’ of Mr. E. Schmidt to get a complete, orthogonal, and normalised set possessing the property (3). 1966G. 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.
So orˈthogonalize v. trans., to render orthogonal (and, often, to normalize); orˈthogonalized ppl. a.
1930Ruark & Urey Atoms, Molecules & Quanta 747 Other systems of polynomials often used in wave mechanics are obtained by orthogonalizing the system, p1/2, xp1/2, x2p1/2,..where p(x) is a so-called ‘weight function’. 1937Michell & Belz Elem. Math. Analysis II. xvii. 914 If the set of functions ϕk(x)..is orthogonalized by means of the function ψ(x). 1939C. H. Goulden Methods Statistical Analysis xii. 192 If the number of varieties is 21, the numbers would be written out as below..and we would have to use a completely orthogonalized 4 × 4 square..to which the remaining numbers would be added as described above. 1948Brown & Campbell Princ. Servomech. iii. 66 After the initial transformation, certain manipulations enable us to orthogonalize the mathematical forms. 1966McGraw-Hill Encycl. Sci. & Technol. II. 93/1 Several techniques exist for solving the wave equation, at least for certain states, notably the Wigner-Seitz method and the orthogonalized-plane-wave method. |
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单词 orthogonally 释义 orthogonally, adv.[f. orthogonal a. + -ly2.]In an orthogonal manner......