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.