# orthogonal

[awr-thog-uh-nl] /ɔrˈθɒg ə nl/
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
1565-1575
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
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2015.
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Examples from the Web for orthogonal
Contemporary Examples
• And that brings up another question about those bacterial targets, the ones that are so orthogonal to human cellular pathways.

• Actually, the issue of plural vs. singular is orthogonal to the dilemma she wants to pose.

Historical Examples
• In the first place, each of these figures may be conceived as an orthogonal projection of a closed plane-faced polyhedron.

Eugene S. Ferguson
• The involutes are “orthogonal trajectories” of the tangents to the common evolute.

British Dictionary definitions for orthogonal

## orthogonal

/ɔːˈθɒɡənəl/
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
Collins English Dictionary - Complete & Unabridged 2012 Digital Edition
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012
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Word Origin and History for orthogonal

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
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orthogonal in Science
 orthogonal   (ôr-thŏg'ə-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
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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".
[Jargon File]
(2002-12-02)

The Free On-line Dictionary of Computing, © Denis Howe 2010 http://foldoc.org
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### Word Value for orthogonal

14
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