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Formally, the Mahalanobis distance of a multivariate vector from a group of values with mean and covariance matrix is defined as:

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## Some Related Sentences

Formally and distance

__Formally__

**,**an ultrametric space

**is**

**a**set

**of**points

**with**an associated

__distance__function ( also called

**a**metric )

__Formally__

**,**for received words

**,**let denote

**the**Hamming

__distance__between

**and**

**,**that

**is**

**,**

**the**number

**of**positions in which

**and**differ.

Formally and vector

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__

**,**an inner product space

**is**

**a**

__vector__space V over

**the**field together

**with**an inner product

**,**i. e.,

**with**

**a**map

__Formally__

**,**in

**the**finite-dimensional case

**,**if

**the**linear map

**is**represented

**as**

**a**multiplication by

**a**

**matrix**A

**and**

**the**translation

**as**

**the**addition

**of**

**a**

__vector__

**,**an affine map acting on

**a**

__vector__can be represented

**as**

__Formally__

**,**

**a**transductive support

__vector__machine

**is**

**defined**by

**the**following primal optimization problem

**:**

__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**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__

**,**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__

**,**

**a**complex projective space

**is**

**the**space

**of**complex lines through

**the**origin

**of**an ( n + 1 )- dimensional complex

__vector__space.

__Formally__

**,**

**the**normal bundle to N in M

**is**

**a**quotient bundle

**of**

**the**tangent bundle on M

**:**one has

**the**short exact sequence

**of**

__vector__bundles on N

**:**

Formally and from

Limits

**and**colimits in**a**category C are**defined**by means**of**diagrams in C.__Formally__**,****a**diagram**of**type J in C**is****a**functor__from__J to C**:**
In late 1900s

**the**day that**of****the**City was founded**is**Jakin School**is****a**Private School**is**__Formally__Part**of**Jakin School Board was Grades One through Twelve there**is**no Football field on this school. In 1966 When Jakin School was Closed were Sent to Blakely-Union Elementary**,**Junior High**,****and**High School ( which later Became Early County High**,**Middle**,****and**Elementary School ). while Carver school was built for African-American students grades One through Twelve. although late 1960s when Carver school was closed along**with**Kestler School was based in Damascus were sent to Washington High & Elementary at Blakely. In addition to small farm agriculture**,**Jakin's early economic growth resulted__from__turpentine.__Formally__

**,**bending modulus

**is**

**defined**

**as**

**the**energy required to deform

**a**membrane

__from__its intrinsic curvature to some other curvature.

__Formally__

**,**

**the**word

**is**applied to persons who are publicly accepted in

**a**recognised capacity

**,**such

**as**professional employment

**,**graduation

__from__

**a**course

**of**study

**,**etc., to give critical commentaries in one or any

**of**

**a**number

**of**specific fields

**of**public or private achievement or endeavour.

__Formally__

**,**it

**is**

**a**coalition

**of**U. S.

**and**European CEOs

**,**largely

__from__transnational corporations

**,**launched at

**the**urging

**of**former United States Secretary

**of**Commerce Ron Brown in Seville ( Spain ) in late 1995 at

**a**conference attended by CEOs

__from__more than 100 U. S.

**and**EU companies

**and**by top government representatives led by

**the**Commissioners for Trade

**and**Industry

**and**by

**the**U. S. Secretary

**of**Commerce.

__Formally__reported

__from__November 1944 onwards

**,**witnesses often assumed that

**the**foo fighters were secret weapons employed by

**the**enemy

**,**but they remained unidentified post-war

**and**were reported by both Allied

**and**Axis forces.

__Formally__

**,**under Henry IV

**,**Arundel served twice

**as**Lord Chancellor

**,**first in 1399

**and**again

__from__1407 to 1410.

__Formally__

**,**this follows

__from__

**the**convolution theorem in mathematics

**,**which relates

**the**Fourier transform

**of**

**the**power spectrum (

**the**intensity

**of**each frequency ) to its autocorrelation.

It has been leased

__from__**the**National Trust since 1974 by**the**Somerset Wildlife Trust (__Formally__Somerset Trust for Nature Conservation )**and****is**run**as****a**nature reserve**and**visitor centre.__Formally__this approximation

**is**founded on

**the**variational principle

**,**valid for Hamiltonians that are bounded

__from__below.

__Formally__designated

**as**

**the**Manhattan Engineer District

**,**it refers specifically to

**the**period

**of**

**the**project

__from__1941 – 1946 under

**the**control

**of**

**the**U. S. Army Corps

**of**Engineers

**,**under

**the**administration

**of**General Leslie R. Groves.

* Blades ( hip-hop

**group**) (__Formally__Blades Of Hades ), Australian hip hop**group**__from__Newcastle**,**New South Wales__Formally__known

**as**

**the**Inverurie Parish Church

**,**

**a**split in Church

**of**Scotland over

**the**appointment

**of**ministers in 1843 ( The Disruption ) led to

**the**creation

**of**

**the**West Parish Church ( known locally

**as**" The West Kirk ") which was founded

**as**

**a**Free Church (

**a**church free

__from__Edinburgh control ) thus causing

**the**Inverurie Parish Church to change its name.

__Formally__established in 1475

**,**though in fact much older

**,**it has 75

**,**000 codices

__from__throughout history.

__Formally__

**,**knowing

**the**step response

**of**

**a**dynamical system gives information on

**the**stability

**of**such

**a**system

**,**

**and**on its ability to reach one stationary state when starting

__from__another.

__Formally__known

**as**Mickleham Grand it used to range

__from__Mount Ridley Road to Crestmont Terrace

**,**but now

**is**connected to

**the**urbanised areas

**of**Craigieburn.

__Formally__

**,**

**the**game ( coalitional game ) consists

**of**

**a**finite set

**of**players

**,**called

**the**grand coalition

**,**

**and**

**a**characteristic function denotes

**the**power set

**of**.</ ref >

__from__

**the**set

**of**all possible coalitions

**of**players to

**a**set

**of**payments that satisfies.

__Formally__called "

**the**Wigwam ", this immense edifice was located on Girard Avenue between 19th

**and**20th Streets

**,**across

__from__Philadelphia's Girard College.

Formally and group

__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__

**,**collective noun forms such

**as**“

**a**

__group__

**of**people ” are represented by second-order variables

**,**or by first-order variables standing for sets ( which are well-defined objects in mathematics

**and**logic ).

Informally

**,**G has**the**above presentation if it**is****the**" freest__group__" generated by S subject only to**the**relations R.__Formally__**,****the**__group__G**is**said to have**the**above presentation if it**is**isomorphic to**the**quotient**of****a**free__group__on S by**the**normal subgroup generated by**the**relations R.__Formally__

**,**

**a**ring

**is**an Abelian

__group__( R

**,**+), together

**with**

**a**second binary operation * such that for all

**a**

**,**b

**and**c in R

**,**

__Formally__

**,**

**a**frieze

__group__

**is**

**a**class

**of**infinite discrete symmetry groups for patterns on

**a**strip ( infinitely wide rectangle ), hence

**a**class

**of**groups

**of**isometries

**of**

**the**plane

**,**or

**of**

**a**strip.

__Formally__

**,**

**the**

__group__was called Studiengesellschaft für Geistesurgeschichte ‚ Deutsches Ahnenerbe e. V.

__Formally__

**,**let G be

**a**Coxeter

__group__

**with**reduced root system R

**and**k < sub > v </ sub >

**a**multiplicity function on R ( so k < sub > u </ sub > = k < sub > v </ sub > whenever

**the**reflections σ < sub > u </ sub >

**and**σ < sub > v </ sub > corresponding to

**the**roots u

**and**v are conjugate in G ).

__Formally__

**,**define

**the**set

**of**lines in

**the**plane P

**as**L ( P ); then

**a**rigid motion

**of**

**the**plane takes lines to lines –

**the**

__group__

**of**rigid motions acts on

**the**set

**of**lines –

**and**one may ask which lines are unchanged by an action.

__Formally__Roman Kalyn

**is**now

**the**only member

**of**

**the**

__group__

**,**but de-facto GreenJolly exists in name only.

__Formally__

**,**

**a**redistribution

**of**all agents ’ initial endowments

**of**goods among all agents in

**the**system

**is**

**a**core allocation if no

__group__

**of**agents can redistribute their own initial endowments among themselves so

**as**to improve

**the**satisfaction

**of**someone in

**the**

__group__without impairing that

**of**any other in

**the**

__group__.

__Formally__

**,**this meant that

**the**whole peloton finished out

**of**time limits

**,**but

**the**referees understandably used

**a**rule saying that they could give clemency to any

__group__

**of**more than 20 %

**of**

**the**stage's starting riders

**,**officially citing

**the**weather conditions

**as**their reason to do so.

__Formally__

**,**

**a**signed graph Σ

**is**

**a**pair ( G

**,**σ ) that consists

**of**

**a**graph G = ( V

**,**E )

**and**

**a**sign mapping or signature σ

**from**E to

**the**sign

__group__

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