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orthogonal

Line breaks: or|thog¦on¦al
Pronunciation: /ɔːˈθɒɡ(ə)n(ə)l
 
/

Definition of orthogonal in English:

adjective

1Of or involving right angles; at right angles.
Example sentences
  • Lanczos was much influenced by Fejér; he learnt from him about Fourier series, orthogonal polynomials, and interpolation.
  • As we have noted above, other contributions by Steinhaus were on orthogonal series, probability theory, real functions and their applications.
  • From these beginnings he moved to prove a number of limit theorems, now known as the Szegö limit theorem, the strong Szegö limit theorem and Szegö's orthogonal polynomials and on the unit circle.
2 Statistics (Of variates) statistically independent.
Example sentences
  • Disciplinary infractions were further summarized by entering the 18 remaining codes into a principal-components analysis using an orthogonal rotation.
  • A test of the hypothesis that ß 1 = 1 can be constructed from the orthogonal regression estimate and standard error for 1.
  • Gram is best remembered for the Gram-Schmidt orthogonalisation process which constructs an orthogonal set from an independent one.
2.1(Of an experiment) having variates which can be treated as statistically independent.
Example sentences
  • Participants always sorted on proportion in Experiment 2, with orthogonal or one-dimensional stimulus sets.
  • Taguchi first determines the control factors that go into designing a product, their interdependencies, then generates an orthogonal array specifying the number of experiments required to find the optimal solution.
  • The presence of a dicentric chromosome was confirmed by Southern blot analysis of orthogonal field alternating gel electrophoresis gels.

Origin

late 16th century: from French, based on Greek orthogōnios 'right-angled'.

Derivatives

orthogonality

1
noun
Example sentences
  • The assumption of orthogonality seems to present the fewest difficulties at present.
  • In DB97-13 the orthogonality of the partial great circle girdle with respect to the lineation supports the above interpretation of the apparent symmetry in the c-axis pattern.
  • When Darboux proved the orthogonality of systems of homofocal ovals, he also showed that ovals provide a geometrical interpretation of the addition theorem and that they constitute the algebraic form of the integral solution.

orthogonally

2
adverb
Example sentences
  • The Q y axes of BChl-a in LH1 are, along with the ring, to be coupled strongly, but the orthogonally oriented Q x axes are parallel and do not overlap.
  • The side AB = c is taken as a reference direction in each case, and for mathematical convenience is defined such that [Theta] c is always the largest angle or C projects orthogonally onto line AB and not outside it.
  • Because the two sets of antagonistic IFMs are oriented orthogonally within the thorax, contractions in one set activate the other after a short delay, and the entire system functions as a mechanical resonator.

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