• Support PF! Buy your school textbooks, materials and every day products Here!

Some hermitian operators relations

  • Thread starter merkamerka
  • Start date
  • #1
How can I formally demonstrate this relations with hermitian operators?


[tex](A^{\dagger})^{\dagger}=A [/tex]
[tex](AB)^{\dagger}=B^{\dagger}A^{\dagger} [/tex]
[tex]\langle x|A^{\dagger}y \rangle=\langle y|Ax \rangle ^*[/tex]
[tex]If \ A \ is \ hermitian \ and \ invertible, \ then \ A^{-1} \ is \ hermitian[/tex]

I've tried to prove them taking the definition of hermitian operator or/and considering matrices while operating, but I want something more formal.

Thanks
 
Last edited:

Answers and Replies

  • #2
lanedance
Homework Helper
3,304
2
how about using
[tex]
AA^{-1}= \mathbb{I}
[/tex]
 

Related Threads for: Some hermitian operators relations

  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
0
Views
2K
  • Last Post
Replies
20
Views
3K
Replies
13
Views
5K
Replies
1
Views
796
Replies
2
Views
3K
Top