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left function notation (Definition)

We are said to be using left function notation if we write functions to the left of their arguments. That is, if $\alpha : X \to Y$ is a function and $x \in X$ then $\alpha x$ is the image of $x$ under $\alpha$

Furthermore, if we have a function $\beta : Y \to Z$ then we write the composition of the two functions as $\beta \alpha : X \to Z$ and the image of $x$ under the composition as $\beta \alpha x = (\beta \alpha) x = \beta(\alpha x)$

Compare this to right function notation.




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Other names:  left notation
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Cross-references: right function notation, composition, image, arguments, functions
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This is version 2 of left function notation, born on 2002-01-05, modified 2004-05-01.
Object id is 1349, canonical name is LeftFunctionNotation.
Accessed 5684 times total.

Classification:
AMS MSC03E20 (Mathematical logic and foundations :: Set theory :: Other classical set theory )

Pending Errata and Addenda
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Help on correlation matrix by on 2003-07-30 21:21:26
Hi, Friends,

I had a question here. If we want to define a multi-uniform distribution for the correlation matrix(k*k), which should have a pdf, proportional to 1/(area(correlation matrix)). How should we do?

Property of correlation matrix:
Diagonal element=1;
Symmetric;
Non-diagonal element is [-1,1]
Positive definite

Thanks,
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