- #1
Aradan
- 2
- 0
Hi, I'm new in this forum.
I have a problem i can't solve and searching on Google i couldn't find anything.
It says:
If D(g) is a representation of a finite group of order [itex] n [/itex], show that
[itex] K = \sum^{i=1}_{n} D^{\dagger} (g_i) D(g_i) [/itex] has the properties:
b) All eigenvalues of [itex] K [/itex] are positive
This is to prove that every representation is equivalent to a unitary representation (the problem is from the book of Matthews and Walker, problem 16-22).
I know that [itex] K = K^{\dagger} [/itex] implies that all eigenvalues of [itex] K [/itex] are real, but i can't figure it out how to demonstrate that they are positive also.
Thanks in advance (sorry for muy bad english)
I have a problem i can't solve and searching on Google i couldn't find anything.
It says:
If D(g) is a representation of a finite group of order [itex] n [/itex], show that
[itex] K = \sum^{i=1}_{n} D^{\dagger} (g_i) D(g_i) [/itex] has the properties:
b) All eigenvalues of [itex] K [/itex] are positive
This is to prove that every representation is equivalent to a unitary representation (the problem is from the book of Matthews and Walker, problem 16-22).
I know that [itex] K = K^{\dagger} [/itex] implies that all eigenvalues of [itex] K [/itex] are real, but i can't figure it out how to demonstrate that they are positive also.
Thanks in advance (sorry for muy bad english)