Results 1 to 2 of 2

Math Help - Linear Algebra projection

  1. #1
    Junior Member
    Joined
    May 2012
    From
    NH
    Posts
    26

    Linear Algebra projection

    Suppose E is a projection in M_2(C) with rank one. Show that there is a real number θ and a complex number β with |β| = 1 such that
    E =
    cos^2 βsinθcosθ
    Bsinθcosθ sin^2 θ

    M_2(C) represents an 2 x 2 matrix in the complex numbers.
    Β represents β conjugate.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,389
    Thanks
    1324

    Re: Linear Algebra projection

    It's impossible to be sure what you mean. Is it
    \begin{pmatrix}cos^2(\theta) & \beta sin(\theta)cos(\theta) \\ \overline{\beta}sin(\theta)cos(\theta) & sin^2(\theta)\end{pmatrix}
    ?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Orthogonal projection and linear transformation
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: June 12th 2011, 09:54 AM
  2. Linear projection problem
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: May 5th 2011, 10:24 AM
  3. Projection - linear transformation
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: July 5th 2010, 03:36 PM
  4. Linear Algebra Question (projection, transformation)
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: November 22nd 2009, 12:39 PM
  5. Linear Transfrm. Projection Problem
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: August 24th 2007, 01:51 PM

Search Tags


/mathhelpforum @mathhelpforum