一类杨辉矩阵的逆矩阵

The Inverse of a Class of Yang Hui Matrix

摘要: 通过将对称杨辉矩阵分解为下三角杨辉矩阵与上三角杨辉矩阵的乘积，得到其行列式为1的简单证明；推导下三角杨辉矩阵的逆矩阵公式，由此快速求解对称杨辉矩阵的逆矩阵；揭示对称杨辉矩阵的逆矩阵与上、下三角杨辉矩阵乘积之间的关系。

Abstract: By decomposing the symmetric Yang Hui matrix to the product of lower/upper triangular Yang Hui matrices, a simple proof is given for the fact that its determinant equals to 1; an explicit formula of the inverse of the lower triangular Yang Hui matrix is provided, which yields a rapid method to calculate the inverse of the symmetric Yang Hui matrix; the relations between the inverse of the symmetric Yang Hui matrix and the upper/lower triangular Yang Hui matrices are uncovered.