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Math Help - Problems of pseudoinverse and SVD in linear algebra

  1. #1
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    May 2009
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    Problems of pseudoinverse and SVD in linear algebra

    I am trying to find the pseudo inverse and SVD as well as single values for a matrix:

    Thus far I have been able to (this is condensed a little) the following:

    Matrix A is:
    |1 1 -1|
    |1 1 -1|

    SVD:
    Matrix ATA =

    | 2 2 -2|
    | 2 2 -2|
    |-2 -2 2 |

    This matrix has rank 2 so it must have a 2-D nullspace and hence 0 is a double eignevalue. That is the eigenvalues I found to be as:
    Lamba2,3 =0, Lambda1 =6.

    Thus the corresponding orthonormal eigenvectors are:
    V1=1/sqrt(3)*(|1|
    |1|
    |1|)

    V2=1/sqrt(2)*(|1 |
    |-1|
    | 0|)

    V3=1/sqrt(6)*(|1|
    |1|
    |1|)
    Now:
    Let V=|V1*V2*V3|

    The last two found via satisfying x+y-2z=0 and applying Gram Schmidt to get the orthogonal basis.

    Sum=(|alpha1 0 0|
    | 0 0 0|)*U1=

    Av1/sqrt(6)
    = 1/sqrt(2)*(|1|
    |1|)

    Let U2=1/sqrt(2)*(| 1|
    |-11|) to be a vector orthogogonal to u1, and set
    u1 = to |u1 u2|

    I am trying to finish this problem and it asks to find the Single values, SVD, and Pseudo inverse.
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  2. #2
    Junior Member
    Joined
    May 2009
    Posts
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    Hello, Is anybody out there? I have'nt been able to get working on this problem much lately although..."I did" take it through the entire steps "before" I posted the question!

    Again,
    I seem to have trouble with finding the SVD; Orthogonal vectors made orthonormal but not getting an SVD. Also, my pseudoinverse is not working?

    Any suggestions are totally appreciated Thanks!
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  3. #3
    Junior Member
    Joined
    May 2009
    Posts
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    I got this figured out. There was a great link on the UCD site
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