orthogonal

[awr-thog-uh-nl] /ɔrˈθɒg ə nl/
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.
Origin
1565-75; obsolete orthogon(ium) right triangle (< Late Latin orthogōnium < Greek orthogṓnion (neuter) right-angled, equivalent to ortho- ortho- + -gōnion -gon) + -al1
Related forms
orthogonality, noun
orthogonally, adverb
Examples from the web for orthogonal
  • The interplay between solid and void, transparency and opacity, curved and orthogonal forms.
  • Teaching is pretty much orthogonal to using technology, even if you teach high technology.
  • On this system, goodness and evil were represented as orthogonal to that lawful-chaotic axis.
  • In the view above, the main subduction zone where the plate motions are more orthogonal are further south.
  • They may be admirable, but they are orthogonal to science in general and to evolution in particular.
  • Science should be orthogonal with religion, which is why agnosticism is actually the only belief that is consistent with it.
  • Our privacy rights interfere with industry use and sale of data, or are at best orthogonal to the pursuit of further profits.
  • orthogonal flow often means rain or snow if mountains or fronts are involved, but not always.
  • In no time, correctly orthogonal positions are laid down, and the quarreling resumes.
  • But to suggest they are basically orthogonal is not sensible either.
British Dictionary definitions for orthogonal

orthogonal

/ɔːˈθɒɡənəl/
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
Derived Forms
orthogonally, adverb
Word Origin and History for 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.

orthogonal in Science
orthogonal
  (ôr-thŏg'ə-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.


orthogonal in Technology

geometry
At 90 degrees (right angles).
N mutually orthogonal vectors span an N-dimensional vector space, meaning that, any vector in the space can be expressed as a linear combination of the vectors. This is true of any set of N linearly independent vectors.
The term is used loosely to mean mutually independent or well separated. It is used to describe sets of primitives or capabilities that, like linearly independent vectors in geometry, span the entire "capability space" and are in some sense non-overlapping or mutually independent. For example, in logic, the set of operators "not" and "or" is described as orthogonal, but the set "nand", "or", and "not" is not (because any one of these can be expressed in terms of the others).
Also used loosely to mean "irrelevant to", e.g. "This may be orthogonal to the discussion, but ...", similar to "going off at a tangent".
See also orthogonal instruction set.
[Jargon File]
(2002-12-02)