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Formally, a complex projective space is the space of complex lines through the origin of an ( n + 1 )- dimensional complex vector space.

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## Some Related Sentences

Formally and complex

__Formally__

**,**these reside in

**a**

__complex__separable Hilbert space-variously called

**the**" state

**space**" or

**the**" associated Hilbert

**space**"

**of**

**the**system-that

**is**well defined up to

**a**

__complex__number

**of**norm

**1**

**(**

**the**phase factor ).

__Formally__

**,**

**an**elliptic function

**is**

**a**function meromorphic on for which there exist two non-zero

__complex__numbers and with

**(**in other words

**,**not parallel ), such that and for all

**.**

__Formally__

**,**if

**is**

**an**open subset

**of**

**the**

__complex__plane

**,**

**a**point

**of**

**,**and

**is**

**a**holomorphic function

**,**then

**is**called

**a**removable singularity for if there exists

**a**holomorphic function which coincides with on

**.**

__Formally__

**,**

**the**singular value decomposition

**of**

**an**m ×

**n**real or

__complex__matrix M

**is**

**a**factorization

**of**

**the**form

__Formally__

**,**

**an**analytic function ƒ

**(**z )

**of**

**the**real or

__complex__variables z < sub >

**1**</ sub >,…, z < sub >

**n**</ sub >

**is**transcendental if z < sub >

**1**</ sub >, …, z < sub >

**n**</ sub >, ƒ

**(**z ) are algebraically independent

**,**i

**.**e., if ƒ

**is**transcendental over

**the**field C

**(**z < sub >

**1**</ sub >, …, z < sub >

**n**</ sub >).

__Formally__

**,**complexification

**is**

**a**functor Vect < sub > R </ sup > → Vect < sub > C </ sup >, from

**the**category

**of**real

**vector**spaces to

**the**category

**of**

__complex__

**vector**spaces

**.**

__Formally__

**,**

**the**novel

**is**notable because

**of**its lack

**of**paragraphing

**,**

**a**digressive style

**,**

**the**blending

**of**fact and fiction

**,**very long and

__complex__sentences

**(**one sentence

**is**about 9 pages long ) as well as

**the**inclusion

**of**

**a**set

**of**mysterious and evocative photographs

**,**scattered throughout

**the**book

**,**which enhance

**the**melancholy message

**of**

**the**text

**.**

Formally and space

__Formally__

**,**

**an**inner product

__space__

**is**

**a**

**vector**

__space__V over

**the**field together with

**an**inner product

**,**i

**.**e., with

**a**map

__Formally__

**,**

**a**profinite group

**is**

**a**Hausdorff

**,**compact

**,**and totally disconnected topological group: that

**is**

**,**

**a**topological group that

**is**also

**a**Stone

__space__

**.**

__Formally__

**,**this means symmetry under

**a**sub-group

**of**

**the**Euclidean group

**of**isometries in two or three

**dimensional**Euclidean

__space__

**.**

__Formally__

**,**

**the**question

**of**whether

**the**universe

**is**infinite or finite

**is**whether it

**is**

**an**unbounded or bounded metric

__space__

**.**

__Formally__

**,**Minkowski

__space__

**is**

**a**four-dimensional real

**vector**

__space__equipped with

**a**nondegenerate

**,**symmetric bilinear form with signature < tt >(−,+,+,+)</ tt >

**(**Some may also prefer

**the**alternative signature < tt >(+,−,−,−)</ tt >; in general

**,**mathematicians and general relativists prefer

**the**former while particle physicists tend to use

**the**latter

**.**

__Formally__

**,**it

**is**

**a**norm defined on

**the**

__space__

**of**bounded linear operators between two given normed

**vector**spaces

**.**

__Formally__

**,**

**a**ringed

__space__

**(**X

**,**O < sub > X </ sub >)

**is**

**a**topological

__space__X together with

**a**sheaf

**of**rings O < sub > X </ sub > on X

**.**

__Formally__

**,**

**a**coalgebra over

**a**field K

**is**

**a**

**vector**

__space__C over K together with K-linear maps Δ: C → C ⊗ C and ε: C → K such that

__Formally__

**,**

**an**ultrametric

__space__

**is**

**a**set

**of**points with

**an**associated distance function

**(**also called

**a**metric )

__Formally__

**,**

**a**rigged Hilbert

__space__consists

**of**

**a**Hilbert

__space__H

**,**together with

**a**subspace Φ which carries

**a**finer topology

**,**that

**is**one for which

**the**natural inclusion

__Formally__

**,**

**a**frame on

**a**homogeneous

__space__G / H consists

**of**

**a**point in

**the**tautological bundle G → G / H

**.**

__Formally__

**,**

**an**iterated function system

**is**

**a**finite set

**of**contraction mappings on

**a**complete metric

__space__

**.**

__Formally__

**,**rotational symmetry

**is**symmetry with respect to some or all rotations in m-dimensional Euclidean

__space__

**.**

Formally and is

__Formally__organized vocational programs supported by federal funds allow high school students to gain experience in

**a**field

**of**work which

__is__likely to lead to

**a**full-time job on graduation

**.**

__Formally__

**,**

**the**set

**of**all context-free languages

__is__identical to

**the**set

**of**languages accepted by pushdown automata

**(**PDA ).

More rigorously

**,****the**divergence**of****a****vector**field F at**a**point p__is__defined as**the**limit**of****the**net flow**of**F across**the**smooth boundary**of****a**three**dimensional**region V divided by**the**volume**of**V as V shrinks to p**.**__Formally__**,**__Formally__

**,**

**the**base

__is__known as Naval Support Facility Diego Garcia

**(**

**the**US activity ) or Permanent Joint Operating Base

**(**PJOB ) Diego Garcia

**(**

**the**UK's term ).

__Formally__

**,**there

__is__

**a**clear distinction: " DFT " refers to

**a**mathematical transformation or function

**,**regardless

**of**how it

__is__computed

**,**whereas " FFT " refers to

**a**specific family

**of**algorithms for computing DFTs

**.**

__Formally__

**,**oxidation state

__is__

**the**hypothetical charge that

**an**atom would have if all bonds to atoms

**of**different elements were 100 % ionic

**.**

__Formally__

**,**if M

__is__

**a**set

**,**

**the**identity function f on M

__is__defined to be that function with domain and codomain M which satisfies

*

__Formally__**,**when working over**the**reals**,**as here**,**this__is__accomplished by considering**the**limit as ε → 0 ; but**the**" infinitesimal " language generalizes directly to Lie groups over general rings**.**__Formally__

**,**this sharing

**of**dynamics

__is__referred to as universality

**,**and systems with precisely

**the**same critical exponents are said to belong to

**the**same universality class

**.**

__Formally__

**,**

**a**frame

__is__defined to be

**a**lattice L in which finite meets distribute over arbitrary joins

**,**i

**.**e

**.**every

**(**even infinite ) subset

0.108 seconds.