# Even and odd transformation

1. Dec 26, 2013

### LagrangeEuler

Why $\rho,\rho^2,\rho^3,\rho^4$ are even transformation and $\rho\sigma,\rho^2\sigma,\rho^3\sigma$ are odd transformation. I'm talking about case of $D_4$ group, where $\rho$ is rotation and $\sigma$ is reflection.

2. Dec 27, 2013

### tiny-tim

Hi LagrangeEuler!

What is the definition of even (or odd) transformation?

3. Dec 30, 2013

### LagrangeEuler

Not sure.

4. Dec 30, 2013

### tiny-tim

ok, if you can't give a "mathy" definition, just give an ordinary english explanation (or example), and we'll take it from there

(go back to your notes or your book, if necessary)

5. Dec 30, 2013

### HallsofIvy

Staff Emeritus
tiny-tim's point is, I expect, that you cannot expect to understand any explanation we give as to why a specific transformation is, or is not, even or odd if you do not know what the definition of "even" or "odd" transformation is. And in mathematics definition are "working" definitions- we use the precise words of definitions is proving things. So we would expect to use the precise words of the definitions of "even" and "odd" transformations in proving that certain transformations are even or odd.