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Finding Pseudoinverse (Moore-Penrose) through the One-Sided Inverses

  1. Nov 6, 2013 #1
    1. The problem statement, all variables and given/known data

    I want to calculate the (unique) Moore-Penrose Pseudoinverse by knowing the one-sided inverses of a matrix

    2. Relevant equations

    Consider a matrix such as $$B = \begin{bmatrix}
    1 & 0 & 2 \\
    0 & 1 & 1
    \end{bmatrix}$$ I know how to compute the right inverses (or in the case of ##m\geq n## the left inverses) and have done so; I've obtained the result $$B^{-1}_{R} = \begin{bmatrix}
    1-2c_{1} & -2c_{2} \\
    -c_{1} & 1-c_{2} \\
    c_{1} & c_{2}
    \end{bmatrix}$$.

    3. The attempt at a solution

    However, I now want to calculate the (unique) Moore-Penrose Pseudoinverse, preferably using this right-sided inverse. Clearly, it would have to be one of the right-sided inverses. Using matlab I've found that the Moore-Penrose Pseudo inverse equals ##B_{R}^{-1}## for ##c_{1} = \frac{1}{3}, c_{2} = \frac{1}{6}##. Is there a way I could easily get those correct values of ##c_{1}## and $$c_{2}## (by that I mean without using a tool such as Matlab), as in, find those corresponding to the Moore-Penrose Pseudoinverse?
     
  2. jcsd
  3. Nov 6, 2013 #2

    haruspex

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