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orthogonal

[awr-thog-uh-nl]
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adjective
  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.
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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

orthogonal

adjective
  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
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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

orthogonal

adj.

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.

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Online Etymology Dictionary, © 2010 Douglas Harper

orthogonally in Science

orthogonal

[ôr-thŏgə-nəl]
  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.
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The American Heritage® Science Dictionary Copyright © 2011. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.