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Conversely, one-dimensional orthogonal projectors are extreme points of the set of density operators.

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## Some Related Sentences

Conversely and orthogonal

__Conversely__

**,**given central idempotents a < sub > 1 </ sub >,..., a < sub > n </ sub > in R that

**are**pairwise

__orthogonal__and have sum 1

**,**then R is

**the**direct sum

**of**

**the**rings Ra < sub > 1 </ sub >,…, Ra < sub > n </ sub >.

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 extreme

__Conversely__

**,**surveys conducted among living donors postoperatively and in a period

**of**five years following

**the**procedure have shown

__extreme__regret in a majority

**of**

**the**donors

**,**who said that given

**the**chance to repeat

**the**procedure

**,**they would not

**.**

__Conversely__

**,**if

**the**difference in price is near zero

**,**but

**the**more costly competitor would convey an enormous battlefield advantage through special ammunition

**,**radar fire control and laser range finding

**,**enabling it to destroy enemy tanks accurately at

__extreme__ranges

**,**military planners may choose it instead — based on

**the**same cost effectiveness principle

**.**

__Conversely__

**,**using lenses with much longer focal lengths for portraits results in more

__extreme__flattening

**of**facial features

**,**which also may be objectionable to

**the**viewer

**.**

Conversely and points

Each convex

**set**containing X must ( by**the**assumption that it is convex ) contain all convex combinations**of**__points__in X**,**so**the****set****of**all convex combinations is contained in**the**intersection**of**all convex sets containing X**.**__Conversely__**,****the****set****of**all convex combinations is itself a convex**set**containing X**,**so it also contains**the**intersection**of**all convex sets containing X**,**and therefore**the**sets given by these two definitions must be equal**.**
Equipped with this notion

**of**length**,**a Riemannian manifold is a metric space**,**meaning that it has a distance function d ( p**,**q ) whose value at a pair**of**__points__p and q is**the**distance from p to q**.**__Conversely__**,****the**metric tensor itself is**the**derivative**of****the**distance function ( taken in a suitable manner ).__Conversely__

**,**extra lives

**are**earned by collecting heart

__points__

**,**which

**are**earned by defeating enemies or collecting Hearts

**,**with an extra life earned for every 100

__points__earned

**.**

Any point x gives rise to a continuous function p < sub > x </ sub > from

**the**one element topological space 1 ( all subsets**of**which**are**open ) to**the**space X by defining p < sub > x </ sub >( 1 ) = x**.**__Conversely__**,**any function from 1 to X clearly determines one point:**the**element that it "__points__" to**.**__Conversely__

**,**

__points__

**are**deducted from a panellist who gives " answers which

**are**not only wrong

**,**but pathetically obvious ", typically answers that

**are**generally believed to be true but in fact

**are**not

**.**

__Conversely__

**,**if

**the**length-scale decreases and

**the**physical parameters approach fixed values

**,**then we have ultraviolet fixed

__points__

**.**

__Conversely__

**,**Mark Chapman's England's Amateurs site states that

**the**1908 and 1912 teams were Great Britain

**,**and

__points__to

**the**fact that photographic evidence shows

**the**team playing with

**the**Union flag on their shirts

**.**

__Conversely__

**,**a pixel in a zoomed region

**of**a Buddhabrot image can be affected by initial

__points__from regions far outside

**the**one being rendered

**.**

__Conversely__

**,**iteration may give

**the**appearance

**of**

__points__diverging away from a single point ; this would be

**the**case for an unstable fixed point

**.**

__Conversely__

**,**

**the**perennial strategy may sometimes be

**the**more effective survival strategy

**,**because

**the**plant has a head start every spring with growing

__points__

**,**roots

**,**and stored energy that have survived through

**the**winter

**.**

__Conversely__

**,**any pair

**of**lattice

__points__with this property constitute a fundamental pair

**,**and furthermore

**,**they generate

**the**same lattice

**.**

__Conversely__

**,**Clover

__points__out that

**the**villain

**of**slasher films is often a male whose masculinity

**,**and sexuality more generally

**,**

**are**in crisis

**.**

This rational curve sends

**the**zeros**of**G to each**of****the**coordinate__points__**of**; that is**,**all but one**of****the**vanish for a zero**of**G**.**__Conversely__**,**any rational normal curve passing through**the**n + 1 coordinate__points__may be written parametrically in this way**.**__Conversely__

**,**

**the**histogram for a very bright image with few dark areas and / or shadows will have most

**of**its data

__points__on

**the**right side and center

**of**

**the**graph

**.**

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