[permalink] [id link]

Every vector v in determines a linear map from R to taking 1 to v, which can be thought of as a Lie algebra homomorphism.

from
Wikipedia

## Some Related Sentences

Every and vector

__Every__subset A

**of**the

__vector__space is contained within

**a**smallest convex set ( called the convex hull

**of**A ), namely the intersection

**of**all convex sets containing A

**.**

__Every__

__vector__space has

**a**basis

**,**and all bases

**of**

**a**

__vector__space have the same number

**of**elements

**,**called the dimension

**of**the

__vector__space

**.**

__Every__normed

__vector__space V sits

**as**

**a**dense subspace inside

**a**Banach space ; this Banach space is essentially uniquely defined by V and is called the completion

**of**V

**.**

__Every__finite-dimensional

__vector__space is isomorphic

**to**its dual space

**,**but this isomorphism relies on an arbitrary choice

**of**isomorphism ( for example

**,**via choosing

**a**basis and then

**taking**the isomorphism sending this basis

**to**the corresponding dual basis ).

__Every__random

__vector__gives rise

**to**

**a**probability measure on

**R**< sup > n </ sup > with the Borel

**algebra**

**as**the underlying sigma-algebra

**.**

__Every__continuous function

**in**the function space

**can**

**be**represented

**as**

**a**

**linear**combination

**of**basis functions

**,**just

**as**every

__vector__

**in**

**a**

__vector__space

**can**

**be**represented

**as**

**a**

**linear**combination

**of**basis vectors

**.**

__Every__finite-dimensional Hausdorff topological

__vector__space is reflexive

**,**because J is bijective by

**linear**

**algebra**

**,**and because there is

**a**unique Hausdorff

__vector__space topology on

**a**finite dimensional

__vector__space

**.**

__Every__coalgebra

**,**by (

__vector__space ) duality

**,**gives rise

**to**an

**algebra**

**,**but not

**in**general the other way

**.**

*

__Every__holomorphic__vector__bundle on**a**projective variety is induced by**a**unique algebraic__vector__bundle**.**
For example

**,**second-order arithmetic**can**express the principle "__Every__countable__vector__space has**a**basis " but it cannot express the principle "__Every____vector__space has**a**basis ".
Many principles that imply the axiom

**of**choice**in**their general form ( such**as**"__Every____vector__space has**a**basis ") become provable**in**weak subsystems**of**second-order arithmetic when they are restricted**.**__Every__

__vector__space is free

**,**and the free

__vector__space on

**a**set is

**a**special case

**of**

**a**free module on

**a**set

**.**

Every and v

__Every__one

**of**the infinitely many vertices

**of**G

**can**

**be**reached

**from**

__v__< sub >

**1**</ sub > with

**a**simple path

**,**and each such path must start with one

**of**the finitely many vertices adjacent

**to**

__v__< sub >

**1**</ sub >.

__Every__maximal outerplanar graph satisfies

**a**stronger condition than Hamiltonicity: it is node pancyclic

**,**meaning that for every vertex

__v__and every k

**in**the range

**from**three

**to**the number

**of**vertices

**in**the graph

**,**there is

**a**length-k cycle containing

__v__

**.**A cycle

**of**this length may

**be**found by repeatedly removing

**a**triangle that is connected

**to**the rest

**of**the graph by

**a**single edge

**,**such that the removed vertex is not

__v__

**,**until the outer face

**of**the remaining graph has length k

**.**

* Incandenza Filmography interpretations and other Infinite Jest-inspired works online: " Infinite Jest IV ", " Zero Gravity Tea Ceremony ", " The Medusa

__v__**.**The Odalisque ", " The Cold Majesty**of**the Numb ", " Kinds**of**Light ", " Baby Pictures**of**Famous Dicatators 2: Eschatong ", " Good-Looking Men In Small Clever Rooms That Utilize__Every__Centimeter Of Available Space With Mind-Boggling Efficiency ", " Cage-Planar Version ", " Various Small Flames ", " The Exhibit and the Cage ", " Après-Garde Film ", " For Infinite Jest ", " Sixty Minutes More or Less with Madame Psychosis ", " Hal at Age 4 ", " Poor Yorick Entertainment " poster art__Every__

**vector**space V with seminorm p (

__v__) induces

**a**normed space V / W

**,**called the quotient space

**,**where W is the subspace

**of**V consisting

**of**all vectors

__v__

**in**V with p (

__v__)

When

**a**variable**,**__v__**,**is on the LHS**of**an assignment statement**,**such**as**s ( j ), then s ( j ) is**a**definition**of**__v__**.**__Every__variable (__v__) has at least one definition by its declaration ( V ) ( or initialization ).

Every and determines

__Every__telephone company

**,**whether large or small

**,**

__determines__its own ANAC for each individual central office

**,**

**which**tends

**to**perpetuate the current situation

**of**

**a**mess

**of**overlapping and / or spotty areas

**of**coverage

**.**

__Every__number is

**thought**

**of**

**as**

**a**decimal fraction with the initial decimal point omitted

**,**

**which**

__determines__the filing order

**.**

__Every__structure is associated with

**a**certain quantity

**of**energy

**,**

**which**

__determines__the stability

**of**the molecule or ion ( the lower energy

**,**the greater stability ).

__Every__telephone company

**,**whether large or small

**,**

__determines__its own ringback numbers for each individual central office

**,**

**which**tends

**to**perpetuate the current situation

**of**

**a**mess

**of**overlapping and / or spotty areas

**of**coverage

**.**

__Every__character has three stats

**which**help him

**in**battle: Brawn stat

__determines__weapon damage

**,**Brains affects the effectiveness

**of**super powers

**,**and Toughness is the character's defense

**.**

__Every__March

**,**

**a**68-team

**,**six-round

**,**single-elimination tournament ( commonly called March Madness )

__determines__the national champions

**of**NCAA Division I men's college basketball

**.**

Every and linear

__Every__module over

**a**division ring has

**a**basis ;

__linear__maps between finite-dimensional modules over

**a**division ring

**can**

**be**described by matrices

**,**and the Gaussian elimination algorithm remains applicable

**.**

__Every__time

**a**diode switches

**from**on

**to**off or vice versa

**,**the configuration

**of**the

__linear__network changes

**.**

__Every__smooth ( or differentiable )

**map**φ: M → N between smooth ( or differentiable ) manifolds induces natural

__linear__maps between the corresponding tangent spaces:

*

__Every____linear__combination**of**its components Y =**a**< sub >**1**</ sub > X < sub >**1**</ sub > + … +**a**< sub > k </ sub > X < sub > k </ sub > is normally distributed**.**__Every__sedenion is

**a**real

__linear__combination

**of**the unit sedenions

**1**

**,**< var > e </ var >< sub >

**1**</ sub >, < var > e </ var >< sub > 2 </ sub >, < var > e </ var >< sub > 3 </ sub >, ..., and < var > e </ var >< sub > 15 </ sub >,

__Every__physical quantity has

**a**Hermitian

__linear__operator associated

**to**it

**,**and the states where the value

**of**this physical quantity is definite are the eigenstates

**of**this

__linear__operator

**.**

__Every__nontrivial proper rotation

**in**3 dimensions fixes

**a**unique 1-dimensional

__linear__subspace

**of**

**R**< sup > 3 </ sup >

**which**is called the axis

**of**rotation ( this is Euler's rotation theorem ).

__Every__finite-dimensional normed space is reflexive

**,**simply because

**in**this case

**,**the space

**,**its dual and bidual all have the same

__linear__dimension

**,**hence the

__linear__injection J

**from**the definition is bijective

**,**by the rank-nullity theorem

**.**

__Every__bounded

__linear__transformation

**from**

**a**normed

**vector**space

**to**

**a**complete

**,**normed

**vector**space

**can**

**be**uniquely extended

**to**

**a**bounded

__linear__transformation

**from**the completion

**of**

**to**

**.**

__Every__

**vector**

**a**

**in**three dimensions is

**a**

__linear__combination

**of**the standard basis vectors i

**,**j

**,**and k

**.**

__Every__lattice

**in**

**can**

**be**generated

**from**

**a**basis for the

**vector**space by forming all

__linear__combinations with integer coefficients

**.**

__Every__

__linear__program has

**a**dual problem with the same optimal solution

**,**but the variables

**in**the dual problem correspond

**to**constraints

**in**the primal problem and vice versa

**.**

1.246 seconds.