Fast calculation of the Hadamard transform of a 4X4 matrix












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I'm reading a book envolves Hadamard transformations, and in one of the examples they are trying to reconstruct Y from RX+Z where all are 4X4 matrixes.

R is given by:

R= 1/4 * begin{array}{l}5&3&3&-3\3&5&-3&3\3&-3&5&3\-3&3&3&5end{array}
And one step further (without any explanation they write that

H(R) = HRH =
begin{array}{l}2&0&0&0\0&2&0&0\0&0&2&0\0&0&0&-1end{array}

Did they calculate HRH "behind the scenes" or there's a fast way of calculating the transform gives certain characteristics to the matrix?






hadamard-matrices







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    1












    $begingroup$


    I'm reading a book envolves Hadamard transformations, and in one of the examples they are trying to reconstruct Y from RX+Z where all are 4X4 matrixes.

    R is given by:

    R= 1/4 * begin{array}{l}5&3&3&-3\3&5&-3&3\3&-3&5&3\-3&3&3&5end{array}
    And one step further (without any explanation they write that

    H(R) = HRH =
    begin{array}{l}2&0&0&0\0&2&0&0\0&0&2&0\0&0&0&-1end{array}

    Did they calculate HRH "behind the scenes" or there's a fast way of calculating the transform gives certain characteristics to the matrix?






    hadamard-matrices







    share|cite|improve this question











    $endgroup$















      1












      1








      1





      $begingroup$


      I'm reading a book envolves Hadamard transformations, and in one of the examples they are trying to reconstruct Y from RX+Z where all are 4X4 matrixes.

      R is given by:

      R= 1/4 * begin{array}{l}5&3&3&-3\3&5&-3&3\3&-3&5&3\-3&3&3&5end{array}
      And one step further (without any explanation they write that

      H(R) = HRH =
      begin{array}{l}2&0&0&0\0&2&0&0\0&0&2&0\0&0&0&-1end{array}

      Did they calculate HRH "behind the scenes" or there's a fast way of calculating the transform gives certain characteristics to the matrix?






      hadamard-matrices







      share|cite|improve this question











      $endgroup$




      I'm reading a book envolves Hadamard transformations, and in one of the examples they are trying to reconstruct Y from RX+Z where all are 4X4 matrixes.

      R is given by:

      R= 1/4 * begin{array}{l}5&3&3&-3\3&5&-3&3\3&-3&5&3\-3&3&3&5end{array}
      And one step further (without any explanation they write that

      H(R) = HRH =
      begin{array}{l}2&0&0&0\0&2&0&0\0&0&2&0\0&0&0&-1end{array}

      Did they calculate HRH "behind the scenes" or there's a fast way of calculating the transform gives certain characteristics to the matrix?






      hadamard-matrices




      hadamard-matrices






      share|cite|improve this question















      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited Jan 6 at 9:15







      DsCpp

















      asked Jan 6 at 9:03









      DsCppDsCpp

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