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Linear transformation (8460 bytes)
1: ...ector spaces, or, in other words, it "preserves [[linear combination]]s". 5: ...e say that ''f'' : ''V'' → ''W'' is a linear transformation if for any two vectors ''x'' and ''y'' in ''V'' a... 8: ...equivalent to saying that ''f'' "preserves linear combinations", i.e., for any vectors ''x''<sub>1<... 11: ...map '''C''' → '''C''', but it is not '''C'''-linear. 15: * An example of a linear transformation from R<sup><var>3</var></sup> to R<sup><var>4</va... Transformation (2023 bytes) 2: [[de:Transformation]] 3: *'''Transformation''' has two meanings in [[molecular biology]]: 4: **[[Transformation (genetics)|Transformation]] is the genetic alteration of a [[cell (biology)... 5: **Transformation is also the process by which normal cells are con... 6: ...], [[transformation group]]; also [[infinitesimal transformation]]. Transformation (novel) (200 bytes) 1: ''Transformation'' is a [[2000]] [[novel]] by [[Carol Berg]]. It ... 7: [[Category:Fantasy books|Transformation]] Lorentz transformation (6521 bytes) 1: The '''Lorentz transformation''' (LT), named after its discoverer, the Dutch [[... 3: ...s is in contrast to the more intuitive [[Galilean transformation]], which is sufficient at non-relativistic speeds... 5: ...n. If ''c'' is taken to be infinite, the Galilean transformation is recovered, so it may be identified as a limiti... 7: The Lorentz transformation is a [[group transformation]] that is used to transform the space and time co... 8: then these are related according to the Lorentz transformation in the following way: Transformation geometry (833 bytes) 2: In [[mathematics]], '''transformation geometry''' is a name for a pedagogic theory for ... 4: ...)|matrix]] computations are required. The tide of transformation geometry retreated, leaving behind some [[Vector ... Transformation semigroup (2631 bytes) 13: * of a '''semigroup S''' is by '''transformations''' of a state-set Q. 18: ... = |S|+1 states suffice for its representation by transformations of Q : either Q = S , or 24: ...sformations of a (state-) set implies the name '''transformation semigroup''' , and its essential importance for t... 26: ...ot* commutative, since ab and ba may be different transformations of Q, just as ''f(g(x)) =/= g(f(x))'' in general... 28: ''Transformation Semigroups'' form the basic algebra for '''Finite... Transformation problem (4214 bytes) 1: A <b>transformation problem</b> for [[Marxist]] [[political economy]]... 3: ...ore recognisable, everyday prices. This attempted transformation, Bortkiewicz suggests, is unconvincing: in Marx’s... 9: The pivotal moment of transformation in Capital III, from values to an intermediary 'p... 14: ...cance lies in the various responses raised to the transformation problem critique by Marx supporters. Given the ov... 17: The "transformation problem" critique has had more impact within Marx... Transformation language (349 bytes) 1: A '''transformation language''' is a [[computer language]] designed t... 3: [[Macro]] languages are a kind of transformation languages. 8: [[Category:Transformation languages|*]] Projective transformation (58542 bytes) 1: ...e important in projective geometry. A projective transformation can also be called a '''projectivity'''. 3: A projective transformation can be in the (real) one-dimensional [[projective... 5: ==Transformations on the Projective Line== 6: ...lane which contains the ''x''-axis upon which the transformation will be performed. 13: ...tic]] description of a one-dimensional projective transformation. It is now desired to convert it to an [[analyti... Householder transformation (1916 bytes) 1: .... In general [[Euclidean space]] it is a [[linear transformation]] that describes a reflection in a [[hyperplane]]... 3: The Householder transformation was introduced 1958 by [[Alston Scott Householder... 9: ...th>I</math> is the [[identity matrix]] the linear transformation described above is given by the '''Householder ma... 23: ...nd then recursing down the (''i'',''i'') [[minor (linear algebra)|minor]]s of that product. See the [[QR d... 26: [[de:Householdertransformation]] Affine transformation (6185 bytes) 1: ...ween two [[vector space]]s consists of a [[linear transformation]] followed by a [[translation (geometry)|translat... 3: ...mbinations. An '''[[affine combination]]''' is a linear combination in which the sum of the coefficients ... 5: ... adding a constant vector to every element of the linear subspace. 6: ...f a vector space is a subset that is closed under linear combinations; an affine subspace is one that is c... 8: ... ''v''<sub>2</sub>, .., ''v''<sub>''n''</sub> are linearly dependent if scalars Infinitesimal transformation (3215 bytes) 3: ... form of ''small'' [[transformation (mathematics)|transformation]]. For example one may talk about an '''[[infinit... 9: ...a]] are exactly those definitive of infinitesimal transformations, just as the axioms of [[group theory]] embody [... 13: The earliest example of an infinitesimal transformation that may have been recognised as such was in '''E... 25: ... information is in fact coded in an infinitesimal transformation that is a [[first-order differential operator]]. 35: ...it shows in effect that ''D'' is an infinitesimal transformation, generating translations of the real line via the... Natural transformation (9036 bytes) 1: ... [[functor category|functor categories]]. Natural transformations are, after categories and functors, one of the m... 5: ...the categories ''C'' and ''D'', then a '''natural transformation''' η from ''F'' to ''G'' associates to every ... 7: ...[Image:Natural_trafo.png|diagram defining natural transformations]]</div> 9: ...rizontal arrow is reversed. If η is a natural transformation from ''F'' to ''G'', we also write η : ''F'' ... 27: ...eration is a functor, and the maps form a natural transformation from the identity functor to the double dual func... Parity transformation (857 bytes) 1: In [[physics]], '''parity transformation''' is the simultaneous sign flip of all coordinat... 5: ...sional spaces, it is usual to redefine the parity transformation so that it flips the sign of an ''odd'' number of... 7: In [[quantum mechanics]], the parity transformation <math>P</math> becomes an operator that squares t... Transformation matrix (5414 bytes) 1: ...n [[linear algebra]] and [[geometry]], a [[linear transformation]] can be represented by [[matrix multiplication]]... 7: ...ations much easier, such as for [[compositions of transformations]]. 11: ...ed using a 3×3 transformation matrix. Such transformations are useful, for example, in [[2D computer graphi... 15: ... all points <math>(x,y)</math>. The corresponding transformation matrix calculation is: 49: ===Composite transformations=== Transformation theory (2347 bytes) 1: '''Transformation theory''', first explained by [[George Land]] (al... Tschirnhaus transformation (1817 bytes) 1: ...ry)|primitive element]]. This is the most general transformation of an [[irreducible polynomial]] that takes a roo... 15: ...a; over ''K'', we can call ''Q'' a '''Tschirnhaus transformation''' of ''P''. 17: ...hen described (in one way) as all the Tschirnhaus transformations of ''P'' to itself. Fisher transformation (644 bytes) 1: ...ing population, can be tested using the '''Fisher transformation''' applied to ''r''. 3: ==Definition of the Fisher transformation== 5: Let ''N'' be the sample size. The transformation is defined by: Transformation (genetics) (1329 bytes) 1: ...ncorporation efficiency much more. An example of transformation is bT [[cotton]], which incorporates BT genes whi... Conformal transformation (845 bytes) 1: ...ndent scalar function.The importance of conformal transformations for [[electromagnetism]] was brought to light by... 3: ...], the [[Group (mathematics)|group]] of conformal transformations is the [[special orthogonal group]] 7: ...pace: all [[holomorphic function]]s are conformal transformations, except where their derivative is zero.
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