Using elementary symmetric function and complete symmetric function, two kinds generalized Vandermonde matrices are introduced. The relationship between Vandermonde matrices and the generalized Vandermonde matrices is discussed, and the LU factorization of the generalized Vandermonde matrices is obtained. 利用对称函数引入了两种广义Vandermonde矩阵,讨论了Vandermonde矩阵与广义Vandermonde矩阵之间的关系,并得到了广义Vandermonde矩阵的LU分解。
Schur-Concavity of Quotient for the Elementary Symmetric Function and Its Application 初等对称函数商的Schur-凹性及其应用