9203224f   
   From: D.Goncz-A.A.S.M.E.T.-CPS-NPI1659534493@replikon.net   
      
   Let's consider square matrices   
      
   The identity matrix is a diagonal from upper left to lower right of all   
   ones   
      
   The transpose matrix is, if I remember Wikipedia correctly gosh I'm sorry,   
   a single diagonal from upper right to lower left of all ones   
      
   Clearly the transpose of the transpose is identity making transpose the   
   second square root of the identity matrix   
      
   Let us consider now   
      
   The negative identity matrix with a diagonal from upper left to lower right   
   of all negative ones   
      
   Multiplying by this twice and gives identity so it is yet another square   
   root of the identity matrix   
      
   Consider now the negative transpose matrix with a diagonal from upper right   
   to lower left of all negative one s. Multiplying by this twice gives the   
   original matrix. So we see that the negative transpose matrix is yet   
   another square root of the identity matrix.   
      
      
   I wonder if these four square roots of unity   
      
   Can be extended to interpret the negative identity matrix as something   
   which itself might have a square root. My guess is the imaginary identity   
   matrix with a diagonal from upper left to lower right of all i, where I is   
   the square root of negative one, would suffice   
      
      
   Many thanks to John Baez to introducing me to the matrix multiplication   
   operation around a dozen years ago thanks again   
      
      
   [[Mod. note -- Wikipedia has lots of information about matrix square roots:   
     https://en.wikipedia.org/wiki/Square_root_of_a_matrix   
   -- jt]]   
      
   --- SoupGate-Win32 v1.05   
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