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docnet
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- Homework Statement
- psb
- Relevant Equations
- psb
$$F(F(x,y))=(z,w)$$
is the map given by
$$x=z$$
$$y=w$$
No. The map is given if you express ##z=z(u,v)=z(u(x,y),v(x,y))=z(x,y)##. You have to substitute the ##u,v## with their definitions in terms of ##x,y##.docnet said:Homework Statement:: psb
Relevant Equations:: psb
View attachment 278552Solution attempt:
$$F(F(x,y))=(z,w)$$
is the map given by
$$x=z$$
$$y=w$$
I assume after the substitution he got this resultfresh_42 said:You have to substitute the with their definitions in terms of .
Maybe, but I guess there is no way but calculation to be sure. It looks a bit like a local Lie group.mitochan said:I assume after the substitution he got this result
##F^2=E##
##F=F^{-1}##
I corrected it. Idempotent functions are ##F^2=F##. We have theoretically ##F^3=F## and any element with ##F^n=F## qualifies to be idempotent, but Wiki said idempotent functions are those with ##n=2##.mitochan said:Thanks. And for this special idempotent transformation, is it used in Physics ?
The transformation for (x,y)=(-1,0) ## u(-1,0)=-1, v(-1,0)=0##, otherwise as above mentioned would be defined for all xy, uv plane.docnet said:Although my answer is probably wrong, because is not defined everywhere on the plane to start with. I wonder if the composite map would be different if I computed everything out?
A multivariate function is a mathematical function that takes in multiple variables as inputs and produces a single output. It is also known as a multivariable function or a function of several variables.
To find the composition of a multivariate function with itself, you need to substitute the original function into itself. This means that the output of the first function will become the input of the second function, and the resulting output will be the composition of the two functions.
Finding the composition of a multivariate function with itself is important because it allows us to simplify complex functions into a single function. This can make it easier to analyze and solve problems involving the function.
Yes, there are a few rules to follow when finding the composition of a multivariate function with itself. The most important rule is to ensure that the input and output variables of the two functions match up correctly. Additionally, you may need to apply the chain rule or other differentiation techniques to simplify the function.
Yes, the composition of a multivariate function with itself can be applied to any type of function as long as the input and output variables match up correctly. This includes polynomial functions, exponential functions, trigonometric functions, and more.