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Singular Value Decomposition

  1. Feb 25, 2009 #1
    1. The problem statement, all variables and given/known data
    Let A be a real mxn matrix, m>=n, with singular values [tex]\sigma[/tex]j.Show that the singular values of ([tex]\stackrel{I_{n}}{A}[/tex]) are equal to [tex]\sqrt{1+\sigma_j^2}[/tex].


    2. Relevant equations



    3. The attempt at a solution
    I know that an SVD for A is A = U([tex]\stackrel{\Sigma}{0}[/tex])v^T and so, the singular values of A are [tex]\sigma_j[/tex]. I have no idea how to break this down. I assume I want to look at an SVD for ([tex]\stackrel{I_n}{A}[/tex]), but I don't know how to figure out that the singular values would be [tex]\sqrt{1+\sigma_j^2}[/tex]. Does anyone have any ideas? Thanks so much.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
    Last edited by a moderator: Feb 25, 2009
  2. jcsd
  3. Feb 25, 2009 #2
    Also, sorry, I'm having a hard time figuring out how to have it typeset correctly to show you guys what's going on.
     
  4. Feb 25, 2009 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Don't use the html tags and inside LaTex. Use _ for subscripts and ^ for superscripts.
     
  5. Feb 25, 2009 #4
    Oh wow, thank you so much. It looks great.
     
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