Results 1 to 2 of 2

Math Help - Tangent Space of the group of Unitary matrices.

  1. #1
    Junior Member
    Joined
    Apr 2008
    Posts
    48

    Tangent Space of the group of Unitary matrices.

    Hi, I'm having trouble starting out with this question:

    "What is/Define the tangent space of U(n) at the identity matrix?"

    If anyone could give me a hint at how to start working this out I'd be most appreciative.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by skamoni View Post
    Hi, I'm having trouble starting out with this question:

    "What is/Define the tangent space of U(n) at the identity matrix?"

    If anyone could give me a hint at how to start working this out I'd be most appreciative.

    This is Lie groups, manifolds and etc. stuff, and if you haven't yet studied this it may look like chinese to you: the tangent space of U(n) at the unit element is just the space of all anti-hermitian matrices.
    You may try to read the following:
    http://math.ipm.ac.ir/shahshahani/diff/chapter1.pdf
    What you want is at the beginning of page 13, but you need a rather decent load of background in higher maths to udnerstand it.

    Tonio
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Tangent Space in Lie Group
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: May 10th 2014, 06:46 AM
  2. Unitary matrices
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: January 3rd 2011, 05:15 AM
  3. Unitary Matrices
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: March 29th 2010, 04:28 PM
  4. Basis of the tangent space of unitary matrices
    Posted in the Differential Geometry Forum
    Replies: 5
    Last Post: November 15th 2009, 12:42 PM
  5. Replies: 3
    Last Post: November 11th 2009, 06:52 AM

Search Tags


/mathhelpforum @mathhelpforum