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Conversely, every positive semi-definite matrix is the covariance matrix of some multivariate distribution.

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## Some Related Sentences

Conversely and every

__Conversely__

**,**

__every__point on

**the**line can be interpreted as a number in an ordered continuum which includes

**the**real numbers

**.**

__Conversely__

__every__partition

**of**comes from an equivalence relation in this way

**,**according to which if and only if and belong to

**the**same set

**of**

**the**partition

**.**

__Conversely__

**,**

__every__formally real field can be equipped with a compatible total order

**,**that will turn it into an ordered field

**.**

__Conversely__

**,**

__every__preorder

**is**

**the**reachability relationship

**of**a directed graph ( for instance

**,**

**the**graph that has an edge from x to y for

__every__pair ( x

**,**y ) with x ≤ y ).

__Conversely__

**,**though

__every__president from Washington to John Quincy Adams can be definitely assigned membership in an Anglican or Unitarian body

**,**

**the**significance

**of**these affiliations

**is**often downplayed as unrepresentative

**of**their true beliefs

**.**

__Conversely__

**,**birds

**of**prey-which show distinct reverse sexual dimorphism — tend to be monogamous for long periods or mate for life ;

**some**species like

**the**Snail kite will choose new mates

__every__year

**,**polygyny

**is**noted in many Harriers and polyandry has been observed in

**the**Harris ' Hawk ( notable for being

**the**only bird

**of**prey to regularly live and hunt in family and social groups ) and

**the**aforementioned Galapagos hawk

**.**

__Conversely__

__every__

**positive**functional φ gives a corresponding inner product < ƒ

**,**g >< sub > φ </ sub > = φ ( g * ƒ ).

We define Thm ( C ) to be

**the**set**of**all formulas that are valid in C**.**__Conversely__**,**if X**is**a set**of**formulas**,**let Mod ( X ) be**the**class**of**all frames which validate__every__formula from X**.**__Conversely__

**,**if we pick

__every__member

**of**

**the**same population with property and ask " what proportion

**of**these have property?

__Conversely__

**,**

__every__admissible statistical procedure

**is**either a Bayesian procedure or a limit

**of**Bayesian procedures

**.**

As stated earlier

**,**an adjunction between categories C and D gives rise to a family**of**universal morphisms**,**one for each object in C and one for each object in D**.**__Conversely__**,**if there exists a universal morphism to a functor G: C → D from__every__object**of**D**,**then G has a left adjoint**.**
It

**is**a fact that**the**ring**is**a principal ideal ring ; that**is****,**for any ideal I in**,**there exists an integer n in I such that__every__element**of**I**is**a multiple**of**n**.**__Conversely__**,****the**set**of**all multiples**of**an arbitrary integer n**is**necessarily an ideal**,**and**is**usually denoted by ( n ).
This ring

**is****the**endomorphism ring**of**A**.**__Conversely__**,**__every__ring ( with identity )**is****the**endomorphism ring**of****some**object in**some**preadditive category**.**__Conversely__

**,**

__every__Polish space

**is**homeomorphic to a G < sub > δ </ sub >- subset

**of**

**the**Hilbert cube

**.**

__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

**.**

__Conversely__

**the**building can be recovered from

**the**BN pair

**,**so that

__every__BN pair canonically defines a building

**.**

__Conversely__

**,**

**the**following characterization

**of**derived functors holds: given a family

**of**functors R < sup > i </ sup >: A → B

**,**satisfying

**the**above

**,**i

**.**e

**.**mapping short exact sequences to long exact sequences

**,**such that for

__every__injective object I

**of**A

**,**R < sup > i </ sup >( I )= 0 for

__every__

**positive**i

**,**then these functors are

**the**right derived functors

**of**R < sup > 0 </ sup >.

Conversely and positive

__Conversely__

**,**in an n-channel enhancement-mode device

**,**a

__positive__gate-to-source voltage

**is**necessary to create a conductive channel

**,**since one does not exist naturally within

**the**transistor

**.**

Given a field ordering ≤ as in Def 1

**,****the**elements such that x ≥ 0 forms a__positive__cone**of**F**.**__Conversely__**,**given a__positive__cone P**of**F as in Def 2**,**one can associate a total ordering ≤< sub > P </ sub > by setting x ≤ y to mean y − x ∈ P**.**This total ordering ≤< sub > P </ sub > satisfies**the**properties**of**Def 1**.**__Conversely__

**,**

**some**have identified low protein intake as a

__positive__factor

**,**protein

**is**among

**the**causes

**of**dietary acidity

**.**

__Conversely__

**,**if M

**is**

__positive__definite

**,**it has an eigendecomposition P < sup >− 1 </ sup > DP where P

**is**unitary

**,**D diagonal

**,**and all diagonal elements

**of**D are real and

__positive__

**.**

__Conversely__

**,**any Hermitian

__positive__semidefinite

**matrix**M can be written as M = A < sup >*</ sup > A ; this

**is**

**the**Cholesky decomposition

**.**

__Conversely__

**,**any choice

**of**μ

**,**full rank

**matrix**U

**,**and

__positive__diagonal entries Λ < sub > i </ sub > yields a non-singular

**multivariate**normal

**distribution**

**.**

__Conversely__

**,**inserting a tube that

**is**too small can result in inability to achieve effective

__positive__pressure ventilation due to retrograde escape

**of**gas through

**the**glottis and out

**the**mouth and nose ( often referred to as a " leak " around

**the**tube ).

__Conversely__

**,**a number that

**is**greater than zero

**is**called

__positive__; zero

**is**usually thought

**of**as neither

__positive__nor negative

**.**

"

__Conversely__**,**in**the**__positive__sense**,**it would refer to " having it both ways " or " having**the**best**of**both worlds**.**__Conversely__

**,**

**the**film did receive notably

__positive__reviews from such critics as Varietys Derek Elley

**,**A

**.**O

**.**Scott

**of**The New York Times

**,**and online critic James Berardinelli

**.**

__Conversely__

**,**by

**the**Riesz representation theorem

**,**each

__positive__linear form on arises as integration with respect to a Radon measure and

**is**thus a continuous

__positive__linear form on

**.**

__Conversely__

**,**recruiting creatures which share a

__positive__predisposition towards each other increases their morale

**.**

__Conversely__

**,**a down period

**is**characterized by

**the**close being lower than

**the**previous period's ( note that D

**is**nonetheless a

__positive__number ),

__Conversely__

**,**increasing

**the**external K < sup >+</ sup > concentration raises ( more

__positive__)

**the**K < sup >+</ sup > equilibrium potential and produces a

__positive__shift in reversal potential

**.**

__Conversely__

**,**he instituted

__positive__changes

**,**such as longer home leaves and better food and medical / surgical assistance for

**the**troops

**.**

Conversely and matrix

__Conversely__

**,**given any ring

**,**we can form a category by taking objects A < sub > n </ sub > indexed by

**the**set

**of**natural numbers ( including zero ) and letting

**the**hom-set

**of**morphisms from to be

**the**set of-by-matrices over

**,**and where composition

**is**given by

__matrix__multiplication

**.**

__Conversely__

**,**if all surfaces are well separated

**,**all off-diagonal terms can be neglected and hence

**the**whole

__matrix__

**of**

**is**effectively zero

**.**

__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__

**,**it

**is**a consequence

**of**

**the**subsequent conclusions

**of**

**the**theorem that any compact Lie group

**is**isomorphic to a

__matrix__group

**.**

__Conversely__a square

__matrix__

**is**called upper triangular if all

**the**entries below

**the**main diagonal are zero

**.**

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**.**
Statement 4 then implies that a basis

**of**M / mM lifts to a minimal set**of**generators**of**M**.**__Conversely__**,****every**minimal set**of**generators**of**M**is**obtained in this way**,**and any two such sets**of**generators are related by an invertible__matrix__with entries in**the**ring**.**0.172 seconds.