Expectation of scaled identity plus square Wishart matrix

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I found that $mathbf H^tmathbf H$ known as an Wishart matrix,
when each row of $mathbf H$ is an realization of i.i.d. Gaussian random vector of zero mean and identity covariance matrix ($mathbf H$ is square).
Then what is the expectation of $(cmathbf I+mathbf H^tmathbf H)^-1$?
(Expectation of scaled identity plus square Wishart matrix)



For an invert Wishart matrix of tall size, I found that its expectation is well-known as a scaled identity matrix.
However, $mathbf H$ is square and an identity matrix is added in this case.




random-matrices




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    up vote
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    I found that $mathbf H^tmathbf H$ known as an Wishart matrix,
    when each row of $mathbf H$ is an realization of i.i.d. Gaussian random vector of zero mean and identity covariance matrix ($mathbf H$ is square).
    Then what is the expectation of $(cmathbf I+mathbf H^tmathbf H)^-1$?
    (Expectation of scaled identity plus square Wishart matrix)



    For an invert Wishart matrix of tall size, I found that its expectation is well-known as a scaled identity matrix.
    However, $mathbf H$ is square and an identity matrix is added in this case.




    random-matrices




    share|cite|improve this question























      up vote
      1
      down vote

      favorite









      up vote
      1
      down vote

      favorite











      I found that $mathbf H^tmathbf H$ known as an Wishart matrix,
      when each row of $mathbf H$ is an realization of i.i.d. Gaussian random vector of zero mean and identity covariance matrix ($mathbf H$ is square).
      Then what is the expectation of $(cmathbf I+mathbf H^tmathbf H)^-1$?
      (Expectation of scaled identity plus square Wishart matrix)



      For an invert Wishart matrix of tall size, I found that its expectation is well-known as a scaled identity matrix.
      However, $mathbf H$ is square and an identity matrix is added in this case.




      random-matrices




      share|cite|improve this question













      I found that $mathbf H^tmathbf H$ known as an Wishart matrix,
      when each row of $mathbf H$ is an realization of i.i.d. Gaussian random vector of zero mean and identity covariance matrix ($mathbf H$ is square).
      Then what is the expectation of $(cmathbf I+mathbf H^tmathbf H)^-1$?
      (Expectation of scaled identity plus square Wishart matrix)



      For an invert Wishart matrix of tall size, I found that its expectation is well-known as a scaled identity matrix.
      However, $mathbf H$ is square and an identity matrix is added in this case.





      random-matrices





      share|cite|improve this question












      share|cite|improve this question




      share|cite|improve this question








      edited Jul 16 at 2:45









      Michael Hardy

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      asked Jul 16 at 2:17









      DYYANG

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