orthogonal

[ awr-thog-uh-nl ]
/ ɔrˈθɒg ə nl /

adjective

Mathematics.
  1. Also orthographic. pertaining to or involving right angles or perpendiculars: an orthogonal projection.
  2. (of a system of real functions) defined so that the integral of the product of any two different functions is zero.
  3. (of a system of complex functions) defined so that the integral of the product of a function times the complex conjugate of any other function equals zero.
  4. (of two vectors) having an inner product equal to zero.
  5. (of a linear transformation) defined so that the length of a vector under the transformation equals the length of the original vector.
  6. (of a square matrix) defined so that its product with its transpose results in the identity matrix.
Crystallography. referable to a rectangular set of axes.

Origin of orthogonal

1565–75; obsolete orthogon(ium) right triangle (< Late Latin orthogōnium < Greek orthogṓnion (neuter) right-angled, equivalent to ortho- ortho- + -gōnion -gon) + -al1

Related forms

or·thog·o·nal·i·ty, nounor·thog·o·nal·ly, adverb
Dictionary.com Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2019

Examples from the Web for orthogonal

British Dictionary definitions for orthogonal

orthogonal

/ (ɔːˈθɒɡənəl) /

adjective

relating to, consisting of, or involving right angles; perpendicular
maths
  1. (of a pair of vectors) having a defined scalar product equal to zero
  2. (of a pair of functions) having a defined product equal to zero

Derived Forms

orthogonally, adverb
Collins English Dictionary - Complete & Unabridged 2012 Digital Edition © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012

Science definitions for orthogonal

orthogonal

[ ôr-thŏgə-nəl ]

Relating to or composed of right angles.
Relating to a matrix whose transpose equals its inverse.
Relating to a linear transformation that preserves the length of vectors.
The American Heritage® Science Dictionary Copyright © 2011. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.