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Conversely, symmetric tensors are defined as invariants: given the natural action of the symmetric group on the tensor algebra, the symmetric tensors are the subspace on which the symmetric group acts trivially.

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## Some Related Sentences

Conversely and symmetric

__Conversely__

**,**if R is a

__symmetric__relation over a set X

**,**one can interpret it

**as**describing an undirected graph with

**the**elements

**of**X

**as**

**the**vertices and

**the**pairs in R

**as**

**the**edges

**.**

__Conversely__

**,**

**given**a quadratic form in n variables

**,**its coefficients can be arranged into an n × n

__symmetric__matrix

**.**

Thus

**,**b < sub > q </ sub > is a__symmetric__bilinear form over K with matrix A**.**__Conversely__**,**any__symmetric__bilinear form b defines a quadratic form__Conversely__

**,**parahydrogen with an antisymmetric nuclear spin function

**,**can only have rotational wavefunctions that

**are**

__symmetric__with respect to permutation

**of**

**the**two protons

**.**

To summarize

**,**M is a__symmetric__space G / K with a compact isotropy**group**K**.**__Conversely__**,**__symmetric__spaces with compact isotropy**group****are**Riemannian__symmetric__spaces**,**although not necessarily in a unique way**.**

Conversely and are

__Conversely__

**,**experimenters would consider

**as**impressive such statements

**as**

**the**following

**,**

**which**

**,**if they turned out to be hits

**,**

__are__so unusual

**as**to be really significant

**:**

__Conversely__

**,**

**the**vowel marks

**of**

**the**Tigrinya abugida and

**the**Amharic abugida ( ironically

**,**

**the**original source

**of**

**the**term " abugida ") have been so completely assimilated into their consonants that

**the**modifications

__are__no longer systematic and have to be learned

**as**a syllabary rather than

**as**a segmental script

**.**

__Conversely__

**,**most heat-treatable alloys

__are__precipitation hardening alloys

**,**

**which**produce

**the**opposite effects that steel does

**.**

__Conversely__

**,**most realists ( specifically

**,**indirect realists ) hold that perceptions or sense data

__are__caused by mind-independent objects

**.**

__Conversely__

**the**use

**of**true brass seems to have declined in Western Europe during this period in favour

**of**gunmetals and other mixed alloys but by

**the**end

**of**

**the**first Millennium AD brass artefacts

__are__found in Scandinavian graves in Scotland

**,**brass was being used in

**the**manufacture

**of**coins in Northumbria and there is archaeological and historical evidence for

**the**production

**of**brass in Germany and The Low Countries areas rich in calamine ore

**which**would remain important centres

**of**brass making throughout

**the**medieval period

**,**especially Dinant – brass objects

__are__still collectively known

**as**dinanterie in French

**.**

__Conversely__

**,**many fighter aircraft

**,**such

**as**

**the**F-16

**,**

__are__often used

**as**' bomb trucks ,' despite being designed for aerial combat

**.**

__Conversely__

**,**

**the**Belgian Blue's meat tenderness has been argued to be just

**as**tender because there

__are__a large number

**of**smaller muscle fibers

**.**

__Conversely__

**,**because space is expanding

**,**and more distant objects

__are__receding ever more quickly

**,**light emitted by us today may never " catch up " to very distant objects

**.**

__Conversely__

**,**certain general principles ( for example

**,**neighbourliness

**,**or charity )

__are__seen to be universal and consistent

**.**

__Conversely__

**,**modern biological sciences ( including even concepts such

**as**molecular ecology )

__are__intimately entwined and dependent

**on**

**the**methods developed through biotechnology and what is commonly thought

**of**

**as**

**the**life sciences industry

**.**

__Conversely__beetles

__are__prey

**of**various invertebrates and vertebrates including insects

**,**fish

**,**reptiles

**,**birds and mammals

**.**

__Conversely__

**,**factors that favor plate columns

__are__

**:**presence

**of**solids in feed

**,**high liquid rates

**,**large column diameters

**,**complex columns

**,**columns with wide feed composition variation

**,**columns with a chemical reaction

**,**absorption columns

**,**columns limited by foundation weight tolerance

**,**low liquid rate

**,**large turn-down ratio and those processes subject to process surges

**.**

__Conversely__

**,**computer implementations

__are__significant in applying ideas from discrete mathematics to real-world problems

**,**such

**as**in operations research

**.**

__Conversely__

**,**there

__are__other stars that never rise above

**the**horizon

**,**

**as**seen from any

**given**point

**on**

**the**Earth's surface ( except exactly

**on**

**the**equator ).

__Conversely__

**,**Harris maintains that

**the**fact-value distinction is a confusion

**,**proposing that values

__are__really a certain kind

**of**fact

**.**

If neither A nor B includes

**the**idea**of**existence**,**then " some A__are__B " simply adjoins A to B**.**__Conversely__**,**if A or B do include**the**idea**of**existence in**the**way that " triangle " contains**the**idea " three angles equal to two right angles ", then " A exists " is automatically true**,**and we have an ontological proof**of**A's existence**.**__Conversely__

**,**

**the**tiny meson mass mass differences responsible for meson oscillations

__are__often expressed in

**the**more convenient inverse picoseconds

**.**

__Conversely__

**,**BBC critic Mark Kermode believes that "

**the**movie industries

**of**Britain and America

__are__inextricably intertwined ", citing numerous examples

**of**how Hollywood provides work to British production staff and studios

**,**whilst Britain enables Hollywood to base their prestigious productions at UK studios

**.**

__Conversely__

**,**in functional code

**,**

**the**output value

**of**a function depends only

**on**

**the**arguments that

__are__input to

**the**function

**,**so calling a function f twice with

**the**same value for an argument x will produce

**the**same result f ( x ) both times

**.**

__Conversely__

**,**

**the**bodies

**of**people who had certain medical conditions

__are__useful for research into those conditions

**.**

__Conversely__

**,**if

**the**data

__are__sparse — that is

**,**if only K out

**of**N Fourier coefficients

__are__nonzero — then

**the**complexity can be reduced to O ( K log N log ( N / K )), and this has been demonstrated to lead to practical speedups compared to an ordinary FFT for N / K > 32 in a large-N example ( N = 2 < sup > 22 </ sup >) using a probabilistic approximate algorithm (

**which**estimates

**the**largest K coefficients to several decimal places ).

__Conversely__

**,**rifle bullets can pierce light armor and

__are__easier to shoot accurately

**,**but even a carbine such

**as**

**the**Colt M4 is larger and / or longer than a submachine gun

**,**making it harder to maneuver in close quarters

**.**

__Conversely__

**,**if either

**of**these last two expressions is

**defined**

**,**then so is

**the**other ( and again they

__are__equal ).

Conversely and defined

__Conversely__

**,**when one wants to compute an arbitrary number ( N )

**of**discrete samples

**of**one cycle

**of**a continuous DTFT

**,**it can be done by computing

**the**relatively simple DFT

**of**s < sub > N </ sub >,

**as**

__defined__above

**.**

Given a vector space V over a field K

**,****the**span**of**a set S ( not necessarily finite ) is__defined__to be**the**intersection W**of**all subspaces**of**V**which**contain S**.**W is referred to**as****the****subspace**spanned by S**,**or by**the**vectors in S**.**__Conversely__**,**S is called a spanning set**of**W**.**__Conversely__

**,**using

**the**last line

**as**a definition one shows that

**the**expression so

__defined__is a connection compatible with

**the**metric

**,**i

**.**e

**.**is a Levi-Civita connection

**.**

__Conversely__

**,**a function u

**:**E < sub > 1 </ sub > → E < sub > 2 </ sub >

__defined__

**on**a basis

**of**E < sub > 1 </ sub > can be uniquely extended to a linear function

**.**

A section Γ

**of**dπ**:**TP / G → TM such that Γ**:**TM → TP / G is a linear morphism**of**vector bundles over M**,**can be identified with a principal connection in P**.**__Conversely__**,**a principal connection**as**__defined__above gives rise to such a section Γ**of**TP / G**.**__Conversely__

**,**Lenin

__defined__imperialism

**as**"

**the**highest stage

**of**capitalism ",

**the**era in

**which**monopoly finance capital becomes dominant

**,**forcing nations and corporations to compete for control over resources and markets all over

**the**world

**.**

__Conversely__

**,**if F has characteristic zero

**,**then

**given**an homogeneous polynomial ƒ

**of**degree n

**on**V

**,**

**the**polarization

**of**ƒ is a multilinear function

**on**

**the**n-th Cartesian product

**of**V

**.**The polarization is

__defined__by

where it is understood that d and ω refer to

**the**exterior derivative and a matrix**of**1-forms**,**respectively**,**acting**on****the**components**of**ξ**.**__Conversely__**,**a matrix**of**1-forms ω is a priori sufficient to completely determine**the**connection locally**on****the**open set over**which****the**basis**of**sections e is__defined__**.**__Conversely__

**,**this may be evidence that several distinct linguistic phenomena have been called ideophones

**,**and that

**the**concept therefore needs to be better

__defined__to be useful in scientific discourse

**.**

__Conversely__

**,**since

**the**existence

**of**T < sup >∗∗</ sup > implies that that

**of**T < sup >∗</ sup >,

**which**in turn implies T is densely

__defined__

**.**

__Conversely__

**,**his villainous personality tends to be that

**of**one who is hardline or militant straight edge

**,**exemplifying

**the**elitist attitudes and superiority complexes —

__defined__by Punk's common mantra during villainous-themed promos that

**,**because he is straight edge

**,**he is " better than you ".

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