What Are Inverse Transformations and Generating Functions?

aggarwal
Messages
5
Reaction score
0
please explain the terms with example:----Transformation,direct transformation,inverse transformation,genreating function
 
Physics news on Phys.org
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.
 
just read your book.
 
thanks a lot....
 
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?
 
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.
 
Last edited:

Thread 'Trouble understanding an online solution to an exercise in Dummit & Foote'

##\textbf{Exercise 10}:## I came across the following solution online: Questions: 1. When the author states in "that ring (not sure if he is referring to ##R## or ##R/\mathfrak{p}##, but I am guessing the later) ##x_n x_{n+1}=0## for all odd $n$ and ##x_{n+1}## is invertible, so that ##x_n=0##" 2. How does ##x_nx_{n+1}=0## implies that ##x_{n+1}## is invertible and ##x_n=0##. I mean if the quotient ring ##R/\mathfrak{p}## is an integral domain, and ##x_{n+1}## is invertible then...
View full post »

Thread 'Questions about non existence of GCDs vs (coimages, cokernels)'

The following are taken from the two sources, 1) from this online page and the book An Introduction to Module Theory by: Ibrahim Assem, Flavio U. Coelho. In the Abelian Categories chapter in the module theory text on page 157, right after presenting IV.2.21 Definition, the authors states "Image and coimage may or may not exist, but if they do, then they are unique up to isomorphism (because so are kernels and cokernels). Also in the reference url page above, the authors present two...
View full post »

Thread 'Decomposition into irreps of compact Lie group'

When decomposing a representation ##\rho## of a finite group ##G## into irreducible representations, we can find the number of times the representation contains a particular irrep ##\rho_0## through the character inner product $$ \langle \chi, \chi_0\rangle = \frac{1}{|G|} \sum_{g\in G} \chi(g) \chi_0(g)^*$$ where ##\chi## and ##\chi_0## are the characters of ##\rho## and ##\rho_0##, respectively. Since all group elements in the same conjugacy class have the same characters, this may be...
View full post »

Similar threads

Inverse Mellin transform of the Gamma function
Replies
4
Views
981
I Quintic Polynomial Tschirnhaus Transform: Possible complex Bring Radicals
Replies
0
Views
2K
I Why should a Fourier transform not be a change of basis?
Replies
43
Views
7K
I Passive Transformation and Rotation Matrix
Replies
1
Views
3K
MHB Combination of Linear Transformations
Replies
2
Views
1K
Inverse transformation matrix entry bounds
Replies
6
Views
2K
Why is the heaviside function in the inverse Laplace transform of 1?
Replies
8
Views
4K
What is the Inverse Laplace Transform of e^(-sx^2/2)?
Replies
10
Views
2K
I Follow-up on Index notation for inverse Lorentz transform
Replies
1
Views
791
I What is difference between transformations and automorphisms
Replies
5
Views
2K

Hot Threads

Recent Insights

Back
Top