1. 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.
  2. 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 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. 2018

British Dictionary definitions for orthogonally


  1. relating to, consisting of, or involving right angles; perpendicular
  2. 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 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

orthogonally in Science


  1. Relating to or composed of right angles.
  2. Relating to a matrix whose transpose equals its inverse.
  3. 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.