Structure of elements of the unitary group

  • Thread starter FunkyDwarf
  • Start date
  • #1
489
0

Main Question or Discussion Point

Hey guys,

I'm having a massive brain freeze here trying to show that for any element g in the unitary group you can always represent it as s*some diagonal matrix*s^-1. The only requirement for an element to be unitary is that its hermitian conjugate is its inverse correct? Any hints/help would be appreciated!

Cheers
-G
 
Last edited:

Answers and Replies

  • #2
  • #3
489
0
Ah i think i see what youre saying, its kind of a basis transformation thing? I sort of understand that (not in a way to provide a proper proof though) but is there a way to arrive at that relation just from the strict definition of a unitary matrix?

Cheers
-G
 
  • #4
18
0
It inevitably follows from a theorem in Linear algebra that states every unitary matrix is diagonalizable. You can probably find it in some L(Alg) textbook or alternatively you can simply google that statement.
 

Related Threads for: Structure of elements of the unitary group

Replies
2
Views
572
Replies
8
Views
6K
  • Last Post
Replies
5
Views
8K
  • Last Post
Replies
1
Views
1K
Replies
4
Views
2K
Replies
7
Views
4K
Replies
3
Views
3K
Replies
9
Views
1K
Top