Solution of four order magic square with algebraic method

The paper begins to the Yang Hui fourth-order magic square and introduces two methods of constructing magic square of fourth-order,they are the Yang Hui method though exchanging the elements of magic and the constructing matrix with elements.By using the method of linear algebra to explore the solution of fourth-order magic squares and establishing a constraint equations of fourth-order magic square to obtain the equivalent constraints of equations though elementary transformation.The paper obtains the equivalence relation of four order by using these constraints and the properties of magic squares.Though the above equivalence relation,we made the forth-order magic squares toline transformationandrow transformationand cited the examples to illustrate that how to use the known to get the basic magic square.Finally,the paper described the isomorphic concept of magic square and demonstrated the number of basic solution.As to a known magic square,the paper points that there are eight isomorphic magic squares which including the known magic square.