[ awr-thog-uh-nl ]
/ ɔrˈθɒg ə nl /


  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.

Nearby words

  1. orthogenic,
  2. orthognathia,
  3. orthognathic,
  4. orthognathic surgery,
  5. orthognathous,
  6. orthogonal matrix,
  7. orthogonal projection,
  8. orthogonal trajectory,
  9. orthogonalize,
  10. orthograde

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 formsor·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

British Dictionary definitions for orthogonally


/ (ɔːˈθɒɡənəl) /


relating to, consisting of, or involving right angles; perpendicular
  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 Formsorthogonally, 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

Word Origin and History for orthogonally



1570s, from French orthogonal, from orthogone, from Late Latin orthogonius, from Greek orthogonios "right-angled," from ortho- "straight" (see ortho-) + gonia "angle," related to gony "knee" (see knee (n.)). Related: Orthogonally.

Online Etymology Dictionary, © 2010 Douglas Harper

Science definitions for orthogonally


[ 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.