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orthogonal - 7 dictionary results

or⋅thog⋅o⋅nal

  [awr-thog-uh-nl]
Use orthogonal in a Sentence
–adjective
1. Mathematics.
a. Also, orthographic. pertaining to or involving right angles or perpendiculars: an orthogonal projection.
b. (of a system of real functions) defined so that the integral of the product of any two different functions is zero.
c. (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.
d. (of two vectors) having an inner product equal to zero.
e. (of a linear transformation) defined so that the length of a vector under the transformation equals the length of the original vector.
f. (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; obs. orthogon(ium) right triangle (< LL orthogōnium < Gk orthognion (neut.) right-angled, equiv. to ortho- ortho- + -gōnion -gon ) + -al 1

Related forms:
or⋅thog⋅o⋅nal⋅i⋅ty, noun
or⋅thog⋅o⋅nal⋅ly, adverb
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2009.
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or·thog·o·nal   (ôr-thŏg'ə-nəl)   
adj.  
  1. Relating to or composed of right angles.
  2. Mathematics
    1. Of or relating to a matrix whose transpose equals its inverse.
    2. Of or relating to a linear transformation that preserves the length of vectors.

[From Greek orthogōnios : ortho-, ortho- + gōniā, angle; see genu-1 in Indo-European roots.]
or·thog'o·nal'i·ty (-nāl'ĭ-tē) n., or·thog'o·nal·ly adv.
The American Heritage® Dictionary of the English Language, Fourth Edition
Copyright © 2009 by Houghton Mifflin Company.
Published by Houghton Mifflin Company. All rights reserved.
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Orthogonal

Or*thog"o*nal\, a. [Cf. F. orthogonal.] Right-angled; rectangular; as, an orthogonal intersection of one curve with another.

Orthogonal projection. See under Orthographic.
Webster's Revised Unabridged Dictionary, © 1996, 1998 MICRA, Inc.
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orthogonal

adj. [from mathematics] Mutually independent; well separated; sometimes, irrelevant to. Used in a generalization of its mathematical meaning to describe sets of primitives or capabilities that, like a vector basis in geometry, span the entire `capability space' of the system and are in some sense non-overlapping or mutually independent. For example, in architectures such as the PDP-11 or VAX where all or nearly all registers can be used interchangeably in any role with respect to any instruction, the register set is said to be orthogonal. Or, in logic, the set of operators `not' and `or' is 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 in comments on human discourse: "This may be orthogonal to the discussion, but...."
Jargon File 4.2.0
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Main Entry: or·thog·o·nal
Pronunciation: or-'thäg-&n-&l
Function: adjective
1 a : lying or intersectingat right angles b : being, using, or made with three ECG leads whose axes are perpendicular to each other and to the frontal, horizontal, and sagittal axes of the body orthogonal leads were recorded simultaneously on magnetic tape —Massoud Nemati et al>
2 : statistically independent orthogonal … factors —O. D. Duncan>
Merriam-Webster's Medical Dictionary, © 2002 Merriam-Webster, Inc.
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orthogonal   (ôr-thŏg'ə-nəl)  Pronunciation Key 
  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 © 2002. Published by Houghton Mifflin. All rights reserved.
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orthogonal 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.
[The Jargon File]
(2002-12-02)

The Free On-line Dictionary of Computing, © 1993-2007 Denis Howe
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