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Mapping a matrix to the null space

  1. Mar 19, 2012 #1
    1. The problem statement, all variables and given/known data
    I am trying to run a model in matlab. D is a 2 by 3 matrix, Knowing that DL=0, which means L is mapped to the null space.

    2. Relevant equations
    How can i find L so that it is a 3 by 3 matrix with all its entries being one times a scalar.




    3. The attempt at a solution
    I used null(D) to find L, the solution is a 1X3 matrix (a vector). Since i want a three by three matrix, can i just say that L=[null(D), null(D), null(D)] since L is mapped to the null space(a zeros vector/matrix) thus does not matter if i extend it from a vector to a matrix anyways. Also, can i put an alpha in front of the L to ajust its value so that all its entries equal to 1?
     
  2. jcsd
  3. Mar 19, 2012 #2

    lanedance

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    you may need to give some more info on what you are trying to accomplish

    geomtrically, we can consider the multiplication as follows;
    [tex] D.L = \begin{pmatrix} d_1^T \\ d_2^T \\ \end{pmatrix} \begin{pmatrix} l_1 & l_2 & l_3 \end{pmatrix} [/tex]

    So as the column vectors l_i are perpindcular to all the row vectors d_j, you will have the required matrix.

    Note that if d_1 and d_2 are linearly indpendent, then there will only be one unique l_i, upto a multiplicative constant
     
    Last edited: Mar 19, 2012
  4. Mar 19, 2012 #3
    D is not linearly independent, and L has to be all one times a scalar. How should i ask matlab to build such a matrix?
     
  5. Mar 19, 2012 #4

    lanedance

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