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 Difference between Perpendicular, Orthogonal and Normal linear algebra - What is the difference between orthogonal and . . . Are all eigenvectors, of any matrix, always orthogonal? Eigenvectors of real symmetric matrices are orthogonal orthogonal vs orthonormal matrices - what are simplest possible . . . Eigenvalues in orthogonal matrices - Mathematics Stack Exchange linear algebra - Orthogonal projection of a point onto a line . . .