一个n阶雅可比行列式的值

The Value of An N-Order Jacobian Determinant

摘要: 本文应用矩阵的特征值及秩的性质,给出下列雅可比矩阵的行列式值:
J=((∂y_i)/(∂x_i))_π×π, y_i=(x_i)/???19860314???xk²; i,j=1,2,…,n。
从而把文1的结果推广到n维的情况。所使用的方法比根据行列式基本性质来求值的方法远为简洁。

Abstract: Making use of the properties of eigenvalue and rank of matrices,the value of the determinant of the following Jacobian matrix is given:
J=((∂y_i)/(∂x_j))_n×n, y_i=(x_i)/(???19860314???x_k²); i,j=1,2,...,n; extending the result in1to the case of n-dimensions This method is much simpler than that based on the fundamental properties of determinants.