Sherman-Morrison formula for non-invertible bmatrices

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I am trying to find an expression for inverse of the following matrix




$(L+frac1nJ)$




Where $L$ is the Laplacian of a simple, connected graph with $n$ vertices and $m$ edges, and $J=11^T$ is the all $1$ matrix. It is known that $L$ is singular, while the above matrix is non-singular. Does there exist some formula akin to Sherman–Morrison formula for this kind of inverse computation?







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    up vote
    2
    down vote

    favorite












    I am trying to find an expression for inverse of the following matrix




    $(L+frac1nJ)$




    Where $L$ is the Laplacian of a simple, connected graph with $n$ vertices and $m$ edges, and $J=11^T$ is the all $1$ matrix. It is known that $L$ is singular, while the above matrix is non-singular. Does there exist some formula akin to Sherman–Morrison formula for this kind of inverse computation?







    share|cite|improve this question
























      up vote
      2
      down vote

      favorite









      up vote
      2
      down vote

      favorite











      I am trying to find an expression for inverse of the following matrix




      $(L+frac1nJ)$




      Where $L$ is the Laplacian of a simple, connected graph with $n$ vertices and $m$ edges, and $J=11^T$ is the all $1$ matrix. It is known that $L$ is singular, while the above matrix is non-singular. Does there exist some formula akin to Sherman–Morrison formula for this kind of inverse computation?







      share|cite|improve this question














      I am trying to find an expression for inverse of the following matrix




      $(L+frac1nJ)$




      Where $L$ is the Laplacian of a simple, connected graph with $n$ vertices and $m$ edges, and $J=11^T$ is the all $1$ matrix. It is known that $L$ is singular, while the above matrix is non-singular. Does there exist some formula akin to Sherman–Morrison formula for this kind of inverse computation?









      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited Aug 26 at 20:26









      Omnomnomnom

      122k784170




      122k784170










      asked Jan 26 at 21:23









      Sudipta Roy

      1708




      1708

























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