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In this book, we discuss different types of product on matrices. For example Hadamard product or Schur product (multiplication), Jordan product and triple product. Then we verify algebraic structure and some basic results of matrices with these products. Further we discuss some theorems based on Schur multiplicative maps on Mm,n( ). Also we discuss ideals and spectrum of matrices with these products. We take different norms on Mm,n( ) and we check submultiplicativity of norms with different product. Further, we verify all these norms are equivalent and Mm,n( ) is complete according the norms.