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orthogonal    
a. 直角的,直交的

直角的,直交的

orthogonal
正交的; 垂直的

orthogonal
正交

orthogonal
adj 1: not pertinent to the matter under consideration; "an
issue extraneous to the debate"; "the price was
immaterial"; "mentioned several impertinent facts before
finally coming to the point" [synonym: {extraneous},
{immaterial}, {impertinent}, {orthogonal}]
2: statistically unrelated
3: having a set of mutually perpendicular axes; meeting at right
angles; "wind and sea may displace the ship's center of
gravity along three orthogonal axes"; "a rectangular
Cartesian coordinate system" [synonym: {orthogonal},
{rectangular}]

Orthogonal \Or*thog"o*nal\, a. [Cf. F. orthogonal.]
Right-angled; rectangular; as, an orthogonal intersection of
one curve with another.
[1913 Webster]

{Orthogonal projection}. See under {Orthographic}.
[1913 Webster]

35 Moby Thesaurus words for "orthogonal":
cube-shaped, cubed, cubic, cubiform, cuboid, diced, foursquare,
normal, oblong, orthodiagonal, orthometric, perpendicular, plumb,
plunging, precipitous, quadrangular, quadrate, quadriform,
quadrilateral, rectangular, rhombic, rhomboid, right-angle,
right-angled, right-angular, sheer, square, steep, straight-up,
straight-up-and-down, tetragonal, tetrahedral, trapezohedral,
trapezoid, up-and-down

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)

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....”


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  • Usage of the word orthogonal outside of mathematics
    I always found the use of orthogonal outside of mathematics to confuse conversation You might imagine two orthogonal lines or topics intersecting perfecting and deriving meaning from that symbolize
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    An orthogonal matrix can therefore be thought of as any "coordinate transformation" from your usual orthonormal basis $\ {\hat e_i\}$ to some new orthonormal basis $\ {\hat v_i\} $ You can view other matrices as "coordinate transformations" (if they're nondegenerate square matrices), but they will in general mess with your formula for the "dot
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  • Are all eigenvectors, of any matrix, always orthogonal?
    In general, for any matrix, the eigenvectors are NOT always orthogonal But for a special type of matrix, symmetric matrix, the eigenvalues are always real and eigenvectors corresponding to distinct eigenvalues are always orthogonal
  • linear algebra - Orthogonal projection of a point onto a line . . .
    I wanted to find a direct equation for the orthogonal projection of a point (X,Y) onto a line (y=mx+b) I will refer to the point of projection as as $ (X_p,Y_p)$





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