中文摘要：

本文主要研究了前n-1个顺序主子式均为非零的咒阶方阵的LU分解．作者给出了这类矩阵的LU分解的具体表达式．该表达式由原矩阵中的元素和原矩阵的顺序主子阵的代数余子式给出．最后作者应用这个结果给出了Vandermonde矩阵及其转置矩阵LU分解的具体公式．

英文摘要：

The authors mainly investigate the LU factorization of the squate matrix of order n in which each of its first n-1 ordered principal minor is nonzero. An explicit expression of LU factorization of such matrices is proposed by using the elements of original matrices and algebraic cofactors in the or dered principal submatrices of the original matrix. Finally, applying this result, the authors give explicit formulas of the LU factc;rization of the Vandermonde matrix and its transpose.