orthogonal
adj.
perpendicular, made up of right angles
Orthogonality
In
mathematics, orthogonal, as a simple
adjective, not part of a longer phrase, is a generalization of
perpendicular. It means at
right angles, from the
Greek orthos, meaning "straight", used by Euclid to mean right; and gonia, meaning angle. Two streets that cross each other at a right angle are orthogonal to one another. In recent years, "perpendicular" has come to be used more in relation to right triangles outside of a coordinate plane context, whereas "orthogonal" is used when discussing vectors or coordinate geometry.
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orthogonal
adj.
orthogonal, perpendicular
Orthogonal
(a.)
Right-angled; rectangular; as, an orthogonal intersection of one curve with another.
Webster's Revised Unabridged Dictionary (1913), edited by Noah Porter.
About
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.
[
Jargon File]
(2002-12-02)
(c) Copyright 1993 by Denis Howe