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Formally, this is a solution of the matrix equation by Jacobi iteration.

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## Some Related Sentences

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__

**,**an inner product space

__is__

**a**vector space V over

**the**field together with an inner product

**,**i

**.**e., with

**a**map

__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__

**,**

**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**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

Formally and solution

__Formally__

**,**we have for

**the**approximation to

**the**full

__solution__A

**,**

**a**series in

**the**small parameter ( here called ), like

**the**following:

The Knight Foundation (

__Formally__**the**Foundation for Law and Government ), offers**a**possible__solution__–**the**" Knight 4000 ".

Formally and matrix

__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__

**,**

**the**discrete cosine transform

**is**

**a**linear

**,**invertible function ( where denotes

**the**set

**of**real numbers ), or equivalently an invertible N × N square

__matrix__

**.**

__Formally__

**,**

**the**singular value decomposition

**of**an m × n real or complex

__matrix__M

**is**

**a**factorization

**of**

**the**form

__Formally__

**,**

**the**discrete sine transform

**is**

**a**linear

**,**invertible function F: R < sup > N </ sup > < tt >-></ tt > R < sup > N </ sup > ( where R denotes

**the**set

**of**real numbers ), or equivalently an N × N square

__matrix__

**.**

__Formally__

**,**Aff ( V )

**is**naturally isomorphic to

**a**subgroup

**of**

**,**with V embedded as

**the**affine plane

**,**namely

**the**stabilizer

**of**

**this**affine plane ;

**the**above

__matrix__formulation

**is**

**the**( transpose

**of**)

**the**realization

**of**

**this**

**,**with

**the**( n × n and 1 × 1 ) blocks corresponding to

**the**direct sum decomposition

**.**

__Formally__

**,**let A be

**a**real

__matrix__

**of**which we want to compute

**the**eigenvalues

**,**and let A < sub > 0 </ sub >:= A

**.**

__Formally__

**,**

**the**Mahalanobis distance

**of**

**a**multivariate vector from

**a**group

**of**values with mean and covariance

__matrix__

**is**defined as:

__Formally__

**,**

**the**definition only requires some invertibility

**,**so we can substitute for Q any

__matrix__M whose eigenvalues do not include − 1

**.**

Formally and equation

__Formally__

**,**

**the**

__equation__above defines

**the**macroscopic neutron cross-section ( for reaction x ) as

**the**proportionality constant between

**a**neutron flux incident on

**a**( thin ) piece

**of**material and

**the**number

**of**reactions that occur ( per unit volume ) in that material

**.**

Formally and by

*

__Formally__appoints**the**Prime Minister**of**Finland selected__by__**the**Parliament**,**and formally appoints**the**rest**of****the**cabinet ( Council**of**State ) as proposed__by__**the**Prime Minister__Formally__

**the**Prince-Electors elected

**a**King

**of**

**the**Romans

**,**who was elected in Germany but became Holy Roman Emperor only when crowned

__by__

**the**Pope

**.**

__Formally__

**,**these failed when they were rejected

__by__

**the**Church

**of**England's General Synod in 1972 ; conversations and co-operation continued

**,**however

**,**leading in 2003 to

**the**signing

**of**

**a**covenant between

**the**two churches

**.**

__Formally__

**the**" head

**of**state " can also personally be

**the**" head

**of**government " ( ex officio or

__by__ad hoc cumulation such as an absolute monarch nominating himself ) but otherwise has formal precedence over

**the**Head

**of**Government and other ministers

**,**whether he

**is**their actual political superior ( absolute monarch

**,**executive president ) or rather theoretical or ceremonial in character

**.**

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:__Formally__named " United Press Associations " for incorporation and legal purposes

**,**but publicly known and identified as United Press or UP

**,**it was created

__by__

**the**1907 uniting

**of**three smaller news syndicates

__by__

**the**Midwest newspaper publisher E

**.**W

**.**Scripps

**.**

__Formally__

**,**most

**of**these people were convicted

__by__NKVD troikas (" triplets ")– special courts martial

**.**

__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 ).

__Formally__

**,**

**a**decision problem

**is**P-complete ( complete for

**the**complexity class P ) if it

**is**in P and that every problem in P can be reduced to it

__by__using an appropriate reduction

**.**

__Formally__

**,**we are given

**a**set

**of**hypotheses and

**a**set

**of**manifestations ; they are related

__by__

**the**domain knowledge

**,**represented

__by__

**a**function that takes as an argument

**a**set

**of**hypotheses and gives as

**a**result

**the**corresponding set

**of**manifestations

**.**

__Formally__

**,**

**a**transductive support vector machine

**is**defined

__by__

**the**following primal optimization problem:

__Formally__

**,**DFS

**is**an uninformed search that progresses

__by__expanding

**the**first child node

**of**

**the**search tree that appears and thus going deeper and deeper until

**a**goal node

**is**found

**,**or until it hits

**a**node that has no children

**.**

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**.**0.145 seconds.