Monotonic Transformation Clarification

  • Thread starter Thread starter naturalnumbas
  • Start date Start date
  • Tags Tags
    Transformation
Click For Summary
SUMMARY

A monotonic transformation preserves the order of a function, meaning that if one value is greater than another, the transformation maintains that relationship. In the provided formula, U = (XY) - (XY/(Z+1)), multiplying the entire function by (Z+1) is not a valid monotonic transformation because it alters the function's behavior depending on the variable Z. Therefore, while the transformation may seem acceptable, it does not meet the criteria for monotonicity as it can change the order of outputs based on the value of Z.

PREREQUISITES
  • Understanding of monotonic functions and transformations
  • Familiarity with algebraic manipulation of functions
  • Basic knowledge of variable dependencies in mathematical expressions
  • Concept of order preservation in mathematical functions
NEXT STEPS
  • Study the properties of monotonic functions in detail
  • Explore examples of valid and invalid monotonic transformations
  • Learn about the implications of variable multiplication in function transformations
  • Investigate the concept of order-preserving mappings in mathematics
USEFUL FOR

Mathematicians, students studying calculus or algebra, and anyone interested in the properties of functions and transformations.

naturalnumbas
Messages
6
Reaction score
0
So I understand that a monotonic transformation preserves the order of a function, but I was wondering: could you perform a transformation by multiplying by a variable?

For example the formula:

U = (XY) - (XY/(Z+1))

Is it an acceptable monotonic transformation to multiply the whole function by (Z+1) [assuming X,Y,Z > 0]? I can't see any reason why not, but I can't find a definite answer.

Thanks.
 
Physics news on Phys.org
No dice? Question unclear or just stupid?
 

Similar threads

Link between Z-transform and Taylor series expansion
  • · Replies 2 ·
Replies
2
Views
2K
Probability Density Functions: Transformation of Variables
  • · Replies 3 ·
Replies
3
Views
2K
What does a row matrix represent geometrically?
  • · Replies 8 ·
Replies
8
Views
1K
Prove if ##x<0## and ##y<z## then ##xy>xz## (Rudin)
  • · Replies 2 ·
Replies
2
Views
2K
Fourier transform ##f(t) = te^{-at}##
  • · Replies 6 ·
Replies
6
Views
4K
Laplace transforms for which value of s?
  • · Replies 2 ·
Replies
2
Views
2K
Diff.equation transformation by change of variables
  • · Replies 1 ·
Replies
1
Views
1K
Generalising theta transformation formula from 1-d to m-d
  • · Replies 3 ·
Replies
3
Views
2K
Lagrange multipliers understanding
  • · Replies 8 ·
Replies
8
Views
2K
Is f(z) =(1+z)/(1-z) a real function?
  • · Replies 17 ·
Replies
17
Views
4K