# Definition of *orthogonal* in English:

## orthogonal^{}

### adjective

1Of or involving right angles; at right angles.

*‘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.’**‘Indeed, for AH and BC to be orthogonal, the ratio (H - A) / (B - C) must be purely imaginary.’**‘Other isolated instances of orthogonal polynomials occurring in the work of various mathematicians is mentioned later.’**‘Rotations and reflections are rigid transformations (given by orthogonal mappings) and clearly transform the centroid in the asserted fashion.’**‘Instead of orthogonal geometry, tour guides proudly note that hardly a right-angle is to be found in the extension.’**‘Other methods, such as the use of orthogonal functions, may be used for creation of a surface as well.’**‘Examples are given which illustrate how Ibrahim applied an orthogonal compression to transform a circle into an ellipse, and an oblique compression to map a hyperbola into a second hyperbola.’**‘Two synchronized video cameras record orthogonal planar views of the fins at 250 images per second.’**‘Mathematically speaking, alternate universes are orthogonal; they're located at right angles to each other.’**‘In addition to his work on potential theory and orthogonal set of functions he published a short paper on the problem of the maximum value a n of a positive integer belonging to a set of n positive integers whose reciprocals add to 1.’**‘Bouquet worked on differential geometry, writing on orthogonal surfaces.’**‘Second, geodesics are circular arcs orthogonal to the unit circle.’**‘He studied the problem of orthogonal trajectories, making important contributions by the construction of orthogonal trajectories to families of curves.’**‘Least square means yield values of the dependent variable for every level of each factor from an orthogonal decomposition of the information.’**‘Mercer was a mathematical analyst of originality and skill; he made noteworthy advances in the theory of integral equations, and especially in the theory of the expansion of arbitrary functions in series of orthogonal functions.’**‘The present experiment set out to independently manipulate beliefs and covariation information in an orthogonal design.’**‘His doctoral thesis studied orthogonal systems of functions.’**‘His research concentrated on convergence, in particular convergence of series of orthogonal functions.’*

2Statistics

(of variates) statistically independent.*‘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.’**‘As a result, in populations where the two alleles at each locus are not at equal frequency, many of the genetic effects that are orthogonal in our study population are not statistically independent.’**‘Proteins and peptides would be more accurately defined in high-dimensional space by orthogonal axes representing truly independent characters.’*

- 2.1(of an experiment) having variates which can be treated as statistically independent.
*‘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.’**‘We can exploit the fact that the columns of these matrices must be orthogonal to reduce the number of dimensions in which to search.’**‘The NMI matrix was partitioned into orthogonal patterns of amino acid variability by factor analysis.’*

**Pronunciation**

**Origin**

Late 16th century from French, based on Greek orthogōnios ‘right-angled’.

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