What Are Inverse Transformations and Generating Functions?

[aggarwal]

please explain the terms with example:----Transformation,direct transformation,inverse transformation,genreating function

 

[HallsofIvy]

A transformation, in general, is just a function: y= f(x) "transforms" x to y. In linear algebra at least, a transformation usually means a linear transformation: f(ax+ by)= af(x)+ bf(y). I don't you can use the terms "direct" and "inverse" transformation without more specification. If I start with the transformation f, then its inverse function, f^-1(x) is its "inverse transformation" and I guess one would call f the "direct transformation". Of course, one could as easily think of g(x)=f^-1(x) as the "direct transformation" and its inverse, g^-1(x)= f(x), would be its "inverse transformation".

I don't see what "generating function" has to do with a "transformation".

In general, if you have a sequence of numbers (such as the moments of a probability distribution), then the generating function is the function whose Taylor series has those numbers as coefficients.

 

[mathwonk]

just read your book.

 

[aggarwal]

thanks a lot....

 

[mathwonk]

sorry, it seemed appropriate. maybe if you ask a more precise question that is not specifically answerted in every text, i could help more.

did you actually follow my suggestion, i.e.read your book? if so, where did you get stuck?

 

[Chris Hillman]

Suggest two books

A good book on generating functions is Wilf, Generatingfunctionology, although I feel the "exponential family" stuff is a terrible idea since it utterly obscures what is really going on with the stuff, wreath product and properties of the Joyal cycle index of a structor (aka combintorial species).

Inquiry about direct and inverse transformations plus failure to cite sources in an PF inquiry suggests a certain lack of "mathematical maturity" (to avoid appearance of sarcasm I should perhaps point out that "mathematical maturity" is a commonly used term in mathematics pedagogy at the university level), so Wilf may be too advanced for the OP. However, a good book written for bright high school students (!) on transformations is Yaglom, Geometric Transformations.