Fat matrix inversion

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If G is a MxN fat matrix and S is NxN matrix and both of them are full rank, then what is the inverse of (GSG^T)?
More information about G:
In each row there is exactly one 1 and all other entries are zero.
In each column there is at most one 1 and all other entries are zero.
Example: G =[1 0 0 0;
0 0 1 0;
0 0 0 1]







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    up vote
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    down vote

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    If G is a MxN fat matrix and S is NxN matrix and both of them are full rank, then what is the inverse of (GSG^T)?
    More information about G:
    In each row there is exactly one 1 and all other entries are zero.
    In each column there is at most one 1 and all other entries are zero.
    Example: G =[1 0 0 0;
    0 0 1 0;
    0 0 0 1]







    share|cite|improve this question
























      up vote
      -2
      down vote

      favorite









      up vote
      -2
      down vote

      favorite











      If G is a MxN fat matrix and S is NxN matrix and both of them are full rank, then what is the inverse of (GSG^T)?
      More information about G:
      In each row there is exactly one 1 and all other entries are zero.
      In each column there is at most one 1 and all other entries are zero.
      Example: G =[1 0 0 0;
      0 0 1 0;
      0 0 0 1]







      share|cite|improve this question














      If G is a MxN fat matrix and S is NxN matrix and both of them are full rank, then what is the inverse of (GSG^T)?
      More information about G:
      In each row there is exactly one 1 and all other entries are zero.
      In each column there is at most one 1 and all other entries are zero.
      Example: G =[1 0 0 0;
      0 0 1 0;
      0 0 0 1]









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      share|cite|improve this question








      edited Aug 16 at 1:52

























      asked Aug 16 at 1:47









      Joey

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