orthogonal

adjective or·thog·o·nal \ȯr-ˈthä-gə-n^əl\

Definition of ORTHOGONAL

a : intersecting or lying at right angles

b : having perpendicular slopes or tangents at the point of intersection <orthogonal curves>

: having a sum of products or an integral that is zero or sometimes one under specified conditions: as

a of real-valued functions : having the integral of the product of each pair of functions over a specific interval equal to zero

b of vectors : having the scalar product equal to zero

c of a square matrix : having the sum of products of corresponding elements in any two rows or any two columns equal to one if the rows or columns are the same and equal to zero otherwise : having a transpose with which the product equals the identity matrix

of a linear transformation : having a matrix that is orthogonal : preserving length and distance

: composed of mutually orthogonal elements <an orthogonal basis of a vector space>

: statistically independent

— or·thog·o·nal·i·ty \-ˌthä-gə-ˈna-lə-tē\ noun

— or·thog·o·nal·ly \-ˈthä-gə-n^əl-ē\ adverb

Origin of ORTHOGONAL

Middle French, from Latin orthogonius, from Greek orthogōnios, from orth- + gōnia angle — more at -gon

First Known Use: 1612

Other Mathematics and Statistics Terms

abscissa, denominator, divisor, equilateral, exponent, hypotenuse, logarithm, oblique, radii, rhomb

Medical Dictionary

orthogonal

adjective or·thog·o·nal \ȯr-ˈthäg-ən-^əl\

Medical Definition of ORTHOGONAL

a : lying or intersecting at right angles b : being, using, or made with three ECG leads whose axes are perpendicular to each other and to the frontal, horizontal, and sagittal axes of the body <the three orthogonal leads were recorded simultaneously on magnetic tape—Massoud Nemati et al>

: statistically independent <mental ability may be classified into several orthogonal…factors—O. D. Duncan>