# Definition of orthogonal in English:

## orthogonal

### Pronunciation /ôrˈTHäɡənl//ɔrˈθɑɡənl/

• 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.’
1. 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.’

### Origin

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