The Retainability For Generalized Hadamard Product Of Generalized Square Magic Matrix

In recent years,the research on retainability has already become very active in the matrix theory research field. Because it not only has important theoretical value,but also it can get a lot of studies on the important theory achievement,therefore,the research on retainability was attended by many scholars.In view of retainability for the matrix,firstly,it makes an introduction about the current research situation and achievement in the area of retainability for matrix,square magic square as well as special operations about matrix.Secondly,the definition of the special operations Hadamard product,generalized Hadamard product,magic square matrix and generalized square magic matrix were introduced,and then the definition of generalized difference square magic matrix,generalized non-difference square magic matrix were presented.Finally,on this basis,the retainability for generalized Hadamard product of generalized square magic matrix k2( k33 and k is a natural number) and 2k( k is an odd prime) were discussed,by constructing method and analogy method,theorems and inferences about the retainability for generalized Hadamard product of generalized square magic matrix k2( k33 and k is a natural number) and 2k( k is an odd prime) were obtained,and then makes a discussion about the retainability between generalized difference square magic matrix and generalized non-difference square magic matrix.Through the research on the retainability for generalized Hadamard product of generalized square magic matrix,it provides theoretical supports for square magic square,which makes the structure of square magic square easier.