Research On The Construction And Counting Of Magic Matrix

Magic square,as a special matrix,has always been favored by mathematicians,and its research results are relatively rich.Magic matrix is another kind of special matrix after magic square.There are many contents worth our in-depth study about magic matrix.This thesis will study magic matrix from four aspects.In the first part,the thesis introduces the background and development status of magic matrix,which determines the research significance and necessity of this topic.In the second part,the definition and properties of magic matrix are studied.Firstly,magic matrix are divided into sum-magic matrix,product-magic matrix and sum-product-magic matrix.Secondly,the definitions of these three kinds of magic matrix are given by using matrices.Finally,the properties of magic matrix are divided into matrix properties and linear properties.In the third part,the isomorphism and counting of sum-magic matrix are studied.Firstly,the definition of isomorphism and sum-magic matrix is given,and then the number of isomorphism and sum-magic matrix is given,that is,the counting of sum-magic matrix.In the fourth part,the construction methods of sum-magic matrix and product-magic matrix are studied through the first three parts.The sum-magic matrix is divided into row-sum-magic matrix,column-sum-magic matrix,row-column-sum magic matrix.Then the construction methods of these three kinds of sum-magic matrix are given.Similarly,the product-magic matrix is divided into row-product-magic matrix,column-product-magic matrix and row-column-product-magic matrix,and the corresponding product magic matrix is constructed by using the construction methods of sum-magic matrix.