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взаимнооднозначное отображение

English translation: one-to-one mapping

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Russian term or phrase:взаимнооднозначное отображение
English translation:one-to-one mapping
Entered by: Nik-On/Off
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20:34 Mar 5, 2004
Russian to English translations [PRO]
Science - Science (general) / math
Russian term or phrase: взаимнооднозначное отображение
Переход от матричной записи к независимым скалярным уравнениям индуцируется взаимнооднозначным отображением множества F симметричных матриц на множество H n(2n+1)-мерных векторов
Local time: 09:20
one-to-one mapping
Selected response from:

Alexander Konosov
Russian Federation
Local time: 11:20
Grading comment
4 KudoZ points were awarded for this answer

Summary of answers provided
4 +1one-to-one mapping
Alexander Konosov
3one-to-one transformation
George Vardanyan



42 mins   confidence: Answerer confidence 4/5Answerer confidence 4/5 peer agreement (net): +1
one-to-one mapping


Alexander Konosov
Russian Federation
Local time: 11:20
Works in field
Native speaker of: Native in RussianRussian
PRO pts in category: 4
Grading comment

Peer comments on this answer (and responses from the answerer)
agree  David Knowles: Absolutely!
29 mins
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1 hr   confidence: Answerer confidence 3/5Answerer confidence 3/5
„r„x„p„y„}„~„Ђ„Ђ„t„~„Ђ„x„~„p„‰„~„Ђ„u „Ђ„„„Ђ„q„‚„p„w„u„~„y„u
one-to-one transformation

The implication of example 3 is that, if X has uniform distribution on
(0,1), i.e. a U(0,1) distribution, then Y=F-1(X) has distribution function F.
If we therefore have n independent random values x1,...,xn from a U(0,1)
distribution, and if we calculate yj=F-1(xj) for j=1,...,n, then y1,...,yn are n independent random values from a distributiuon with distribution functiion F.
All programming languages and packages provide a random number
generator which gives a sequence of pseudorandom numbers. These have
the properties of a sequence of independent random values from a U(0,1) distribution.
We can use these pseudorandom numbers x1,...,xn, which may be
considered to be n independent random values from a U(0,1) distribution, to generate independent samples from any continuous distribution.

Using the formal definition, for a transformation T: X ЃЁ Y, onto means
For any y Ѓё Y, there is x Ѓё X, such that (x, y) Ѓё T,
and one-to-one means
(x, y) and (x', y) Ѓё T implies x = x'.

    Reference: http://www.maths.qmw.ac.uk/~lr/stats00n3.pdf
    Reference: http://algebra.math.ust.hk/matrix_linear_trans/09_transforma...
George Vardanyan
Local time: 08:20
Specializes in field
Native speaker of: Native in RussianRussian
PRO pts in category: 4
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