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Schur product for complex numbers.

  1. Nov 1, 2011 #1
    For matrices, Schur product or Hadamard product is defined as the entry wise product.
    I want to know if they have a similar type of multiplication for complex numbers.
    That is (a+ i b) o (c + i d) = (a c + i b d)
    I encounter a situation where such a definition is useful.

    In physics I get an expression that looks like the following

    (Cos[x1] , Cos[x2] ).A.Transpose[(Cos[y1] , Cos[y2] )] +
    i (Sin[x1] , Sin[x2] ).B.Transpose[(Sin[y1] , Sin[y2] )]
    where A and B are 2x2 real matrices.

    I can express the above expression in the following simpler form, if the complex product "o" as I defined earlier already exists in literature.

    (exp[i x1], exp[i x2]) o (A+iB) o Transpose[(exp[i y1], exp[i y2])]

    Thanks very much for the help.
     
  2. jcsd
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